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BEGIN:VEVENT
SUMMARY:Elizabeth Meckes (Case Western Reserve University)
DTSTART:20201013T143000Z
DTEND:20201013T153000Z
DTSTAMP:20260422T225928Z
UID:OxfordRMT/1
DESCRIPTION:Title: Random Matrices with Prescribed Eigenvalues\nby Elizabeth Meckes (Ca
se Western Reserve University) as part of Oxford Random Matrix Theory Semi
nars\n\n\nAbstract\nClassical random matrix theory begins with a random ma
trix model and analyzes the distribution of the resulting eigenvalues. In
this work\, we treat the reverse question: if the eigenvalues are specifi
ed but the matrix is "otherwise random"\, what do the entries typically lo
ok like? I will describe a natural model of random matrices with prescrib
ed eigenvalues and discuss a central limit theorem for projections\, which
in particular shows that relatively large subcollections of entries are j
ointly Gaussian\, no matter what the eigenvalue distribution looks like.
I will discuss various applications and interpretations of this result\, i
n particular to a probabilistic version of the Schur--Horn theorem and to
models of quantum systems in random states. This work is joint with Mark
Meckes.\n\nPlease subscribe to our mailing list (https://lists.maths.ox.ac
.uk/mailman/listinfo/random-matrix-theory-announce) and Zoom link will be
made available the day before.\n
LOCATION:https://researchseminars.org/talk/OxfordRMT/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Meckes (Case Western Reserve University)
DTSTART:20201020T143000Z
DTEND:20201020T153000Z
DTSTAMP:20260422T225928Z
UID:OxfordRMT/2
DESCRIPTION:Title: Comparing counting functions for determinantal point processes\nby M
ark Meckes (Case Western Reserve University) as part of Oxford Random Matr
ix Theory Seminars\n\n\nAbstract\nI will describe a general method for com
paring the counting functions of determinantal point processes in terms of
trace class norm distances between their kernels (and review what all of
those words mean). Then I will outline joint work with Elizabeth Meckes us
ing this method to prove a version of a self-similarity property of eigenv
alues of Haar-distributed unitary matrices conjectured by Coram and Diacon
is. Finally\, I will discuss ongoing work by my PhD student Kyle Taljan\,
bounding the rate of convergence for counting functions of GUE eigenvalue
s to the Sine or Airy process counting functions.\n
LOCATION:https://researchseminars.org/talk/OxfordRMT/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antti Knowles (Université de Genève)
DTSTART:20201027T153000Z
DTEND:20201027T163000Z
DTSTAMP:20260422T225928Z
UID:OxfordRMT/4
DESCRIPTION:Title: Delocalization transition for critical Erdös-Rényi graphs\nby Antt
i Knowles (Université de Genève) as part of Oxford Random Matrix Theory
Seminars\n\n\nAbstract\nWe analyse the eigenvectors of the adjacency matri
x of a critical Erdös-Rényi graph G(N\,d/N)\, where d is of order \\log
N. We show that its spectrum splits into two phases: a delocalized phase i
n the middle of the spectrum\, where the eigenvectors are completely deloc
alized\, and a semilocalized phase near the edges of the spectrum\, where
the eigenvectors are essentially localized on a small number of vertices.
In the semilocalized phase the mass of an eigenvector is concentrated in a
small number of disjoint balls centred around resonant vertices\, in each
of which it is a radial exponentially decaying function. The transition b
etween the phases is sharp and is manifested in a discontinuity in the loc
alization exponents of the eigenvectors. Joint work with Johannes Alt and
Raphael Ducatez.\n\nThis seminar will be held via zoom. Meeting link will
be sent to members of our mailing list (https://lists.maths.ox.ac.uk/mailm
an/listinfo/random-matrix-theory-announce) in our weekly announcement on M
onday.\n
LOCATION:https://researchseminars.org/talk/OxfordRMT/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Bothner (University of Bristol)
DTSTART:20201103T153000Z
DTEND:20201103T163000Z
DTSTAMP:20260422T225928Z
UID:OxfordRMT/5
DESCRIPTION:Title: A threefold way to integrable probabilistic models\nby Thomas Bothne
r (University of Bristol) as part of Oxford Random Matrix Theory Seminars\
n\n\nAbstract\nThis talk is intended for a broad math and physics audience
in particular including students. It will focus on the speaker's recent c
ontributions to the analysis of the real Ginibre ensemble consisting of sq
uare real matrices whose entries are i.i.d. standard normal random variabl
es. In sharp contrast to the complex and quaternion Ginibre ensemble\, rea
l eigenvalues in the real Ginibre ensemble attain positive likelihood. In
turn\, the spectral radius of a real Ginibre matrix follows a different li
miting law for purely real eigenvalues than for non-real ones. We will sho
w that the limiting distribution of the largest real eigenvalue admits a c
losed form expression in terms of a distinguished solution to an inverse s
cattering problem for the Zakharov-Shabat system. This system is directly
related to several of the most interesting nonlinear evolution equations i
n $1+1$ dimensions which are solvable by the inverse scattering method. Th
e results of this talk are based on our joint work with Jinho Baik (arXiv:
1808.02419 and arXiv:2008.01694).\n\nThis seminar will be held via zoom. M
eeting link will be sent to members of our mailing list (https://lists.mat
hs.ox.ac.uk/mailman/listinfo/random-matrix-theory-announce) in our weekly
announcement on Monday.\n
LOCATION:https://researchseminars.org/talk/OxfordRMT/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Theo Assiotis (University of Edinburgh)
DTSTART:20201110T153000Z
DTEND:20201110T163000Z
DTSTAMP:20260422T225928Z
UID:OxfordRMT/6
DESCRIPTION:Title: On the joint moments of characteristic polynomials of random unitary mat
rices\nby Theo Assiotis (University of Edinburgh) as part of Oxford Ra
ndom Matrix Theory Seminars\n\n\nAbstract\nI will talk about the joint mom
ents of characteristic polynomials of random unitary matrices and their de
rivatives. In joint work with Jon Keating and Jon Warren we establish the
asymptotics of these quantities for general real values of the exponents a
s the size N of the matrix goes to infinity. This proves a conjecture of H
ughes from 2001. In subsequent joint work with Benjamin Bedert\, Mustafa A
lper Gunes and Arun Soor we focus on the leading order coefficient in the
asymptotics\, we connect this to Painleve equations for general values of
the exponents and obtain explicit expressions corresponding to the so-call
ed classical solutions of these equations.\n
LOCATION:https://researchseminars.org/talk/OxfordRMT/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nina Snaith (University of Bristol)
DTSTART:20201117T153000Z
DTEND:20201117T163000Z
DTSTAMP:20260422T225928Z
UID:OxfordRMT/7
DESCRIPTION:Title: Zeros\, moments and derivatives\nby Nina Snaith (University of Brist
ol) as part of Oxford Random Matrix Theory Seminars\n\n\nAbstract\nFor 20
years we have known that average values of characteristic polynomials of r
andom unitary matrices provide a good model for moments of the Riemann zet
a function. Now we consider moments of the logarithmic derivative of char
acteristic polynomials\, calculations which are motivated by questions on
the distribution of zeros of the derivative of the Riemann zeta function.
Joint work with Emilia Alvarez.\n
LOCATION:https://researchseminars.org/talk/OxfordRMT/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tom Claeys (Universite catholique de louvain)
DTSTART:20201124T153000Z
DTEND:20201124T163000Z
DTSTAMP:20260422T225928Z
UID:OxfordRMT/8
DESCRIPTION:Title: Asymptotics for averages over classical orthogonal ensembles\nby Tom
Claeys (Universite catholique de louvain) as part of Oxford Random Matrix
Theory Seminars\n\n\nAbstract\nAverages of multiplicative eigenvalue stat
istics of Haar distributed unitary matrices are Toeplitz determinants\, an
d asymptotics for these determinants are now well understood for large cla
sses of symbols\, including symbols with gaps and (merging) Fisher-Hartwig
singularities. Similar averages for Haar distributed orthogonal matrices
are Toeplitz+Hankel determinants. Some asymptotic results for these determ
inants are known\, but not in the same generality as for Toeplitz determin
ants. I will explain how one can systematically deduce asymptotics for ave
rages in the orthogonal group from those in the unitary group\, using a tr
ansformation formula and asymptotics for certain orthogonal polynomials on
the unit circle\, and I will show that this procedure leads to asymptotic
results for symbols with gaps or (merging) Fisher-Hartwig singularities.
The talk will be based on joint work with Gabriel Glesner\, Alexander Mina
kov and Meng Yang.\n
LOCATION:https://researchseminars.org/talk/OxfordRMT/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lisa Hartung (Johannes Gutenberg University Mainz)
DTSTART:20201201T153000Z
DTEND:20201201T163000Z
DTSTAMP:20260422T225928Z
UID:OxfordRMT/9
DESCRIPTION:Title: Maxima of a random model of the Riemann zeta function on longer interval
s (and branching random walks)\nby Lisa Hartung (Johannes Gutenberg Un
iversity Mainz) as part of Oxford Random Matrix Theory Seminars\n\n\nAbstr
act\nWe study the maximum of a random model for the Riemann zeta function
(on the critical line at height T) on the interval $[−(\\log T)^\\theta
\,(\\log T)^\\theta)$\, where $\\theta=(\\log\\log T)−a$\, with $0 < a <
1$. We obtain the leading order as well as the logarithmic correction of
the maximum. \n\nAs it turns out a good toy model is a collection of inde
pendent BRW’s\, where the number of independent copies depends on θ. In
this talk I will try to motivate our results by mainly focusing on this t
oy model. The talk is based on joint work in progress with L.-P. Arguin an
d G. Dubach.\n
LOCATION:https://researchseminars.org/talk/OxfordRMT/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tatyana Shcherbina (University of Wisconsin-Madison)
DTSTART:20210119T153000Z
DTEND:20210119T163000Z
DTSTAMP:20260422T225928Z
UID:OxfordRMT/10
DESCRIPTION:Title: Universality for random band matrices\nby Tatyana Shcherbina (Unive
rsity of Wisconsin-Madison) as part of Oxford Random Matrix Theory Seminar
s\n\n\nAbstract\nRandom band matrices (RBM) are natural intermediate model
s to study eigenvalue statistics and quantum propagation in disordered sys
tems\, since they interpolate between mean-field type Wigner matrices and
random Schrodinger operators. In particular\, RBM can be used to model the
Anderson metal-insulator phase transition (crossover) even in 1d. In this
talk we will discuss some recent progress in application of the supersymm
etric method (SUSY) and transfer matrix approach to the analysis of local
spectral characteristics of some specific types of 1d RBM.\n
LOCATION:https://researchseminars.org/talk/OxfordRMT/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joseph Najnudel (University of Bristol)
DTSTART:20210126T153000Z
DTEND:20210126T163000Z
DTSTAMP:20260422T225928Z
UID:OxfordRMT/11
DESCRIPTION:Title: Secular coefficients and the holomorphic multiplicative chaos\nby J
oseph Najnudel (University of Bristol) as part of Oxford Random Matrix The
ory Seminars\n\n\nAbstract\nWe study the coefficients of the characteristi
c polynomial (also called secular coefficients) of random unitary matrices
drawn from the Circular Beta Ensemble (i.e. the joint probability density
of the eigenvalues is proportional to the product of the power beta of th
e mutual distances between the points). We study the behavior of the secul
ar coefficients when the degree of the coefficient and the dimension of th
e matrix tend to infinity. The order of magnitude of this coefficient depe
nds on the value of the parameter beta\, in particular\, for beta = 2\, we
show that the middle coefficient of the characteristic polynomial of the
Circular Unitary Ensemble converges to zero in probability when the dimens
ion goes to infinity\, which solves an open problem of Diaconis and Gambur
d. We also find a limiting distribution for some renormalized coefficients
in the case where beta > 4. In order to prove our results\, we introduce
a holomorphic version of the Gaussian Multiplicative Chaos\, and we also m
ake a connection with random permutations following the Ewens measure.\n
LOCATION:https://researchseminars.org/talk/OxfordRMT/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karol Życzkowski (Jagiellonian University)
DTSTART:20210202T153000Z
DTEND:20210202T163000Z
DTSTAMP:20260422T225928Z
UID:OxfordRMT/12
DESCRIPTION:Title: Universal spectra of random channels and random Lindblad operators\
nby Karol Życzkowski (Jagiellonian University) as part of Oxford Random M
atrix Theory Seminars\n\n\nAbstract\nWe analyze spectral properties of gen
eric quantum operations\, which describe open systems under assumption of
a strong decoherence and a strong coupling with an environment. In the cas
e of discrete maps the spectrum of a quantum stochastic map displays a uni
versal behaviour: it contains the leading eigenvalue $\\lambda_1 = 1$\, wh
ile all other eigenvalues are restricted to the disk of radius $R<1$. Simi
lar properties are exhibited by spectra of their classical counterparts -
random stochastic matrices. In the case of a generic dynamics in continuou
s time\, we introduce an ensemble of random Lindblad operators\, which gen
erate Markov evolution in the space of density matrices of a fixed size. U
niversal spectral features of such operators\, including the lemon-like sh
ape of the spectrum in the complex plane\, are explained with a non-hermit
ian random matrix model. The structure of the spectrum determines the tran
sient behaviour of the quantum system and the convergence of the dynamics
towards the generically unique invariant state. The quantum-to-classical t
ransition for this model is also studied and the spectra of random Kolmogo
rov operators are investigated.\n
LOCATION:https://researchseminars.org/talk/OxfordRMT/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Nahum (University of Oxford)
DTSTART:20210209T153000Z
DTEND:20210209T163000Z
DTSTAMP:20260422T225928Z
UID:OxfordRMT/13
DESCRIPTION:Title: Random quantum circuits and many-body dynamics\nby Adam Nahum (Univ
ersity of Oxford) as part of Oxford Random Matrix Theory Seminars\n\n\nAbs
tract\nA quantum circuit defines a discrete-time evolution for a set of qu
antum spins/qubits\, via a sequence of unitary 'gates’ coupling nearby s
pins. I will describe how random quantum circuits\, where each gate is a r
andom unitary matrix\, serve as minimal models for various universal featu
res of many-body dynamics. These include the dynamical generation of entan
glement between distant spatial regions\, and the quantum "butterfly effec
t". I will give a very schematic overview of mappings that relate averages
in random circuits to the classical statistical mechanics of random paths
. Time permitting\, I will describe a new phase transition in the dynamics
of a many-body wavefunction\, due to repeated measurements by an external
observer.\n
LOCATION:https://researchseminars.org/talk/OxfordRMT/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jose Moran (University of Oxford)
DTSTART:20210216T153000Z
DTEND:20210216T163000Z
DTSTAMP:20260422T225928Z
UID:OxfordRMT/14
DESCRIPTION:Title: Critically stable network economies\nby Jose Moran (University of O
xford) as part of Oxford Random Matrix Theory Seminars\n\n\nAbstract\nWill
a large economy be stable? In this talk\, I will present a model for a ne
twork economy where firms' productions are interdependent\, and study the
conditions under which such input-output networks admit a competitive econ
omic equilibrium\, where markets clear and profits are zero. Insights from
random matrix theory allow to understand some of the emergent properties
of this equilibrium and to provide a classification for the different type
s of crises it can be subject to. After this\, I will endow the model with
dynamics\, and present results with strong links to generalised Lotka-Vol
terra models in theoretical ecology\, where inter-species interactions are
modelled with random matrices and where the system naturally self-organis
es into a critical state. In both cases\, the stationary points must consi
st of positive species populations/prices/outputs. Building on these ideas
\, I will show the key concepts behind an economic agent-based model that
can exhibit convergence to equilibrium\, limit cycles and chaotic dynamics
\, as well as a phase of spontaneous crises whose origin can be understood
using "semi-linear" dynamics.\n
LOCATION:https://researchseminars.org/talk/OxfordRMT/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yacine Barhoumi (Ruhr-Universität Bochum)
DTSTART:20210223T153000Z
DTEND:20210223T163000Z
DTSTAMP:20260422T225928Z
UID:OxfordRMT/15
DESCRIPTION:Title: A new approach to the characteristic polynomial of a random unitary mat
rix\nby Yacine Barhoumi (Ruhr-Universität Bochum) as part of Oxford R
andom Matrix Theory Seminars\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OxfordRMT/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Diane Holcomb (KTH Stockholm)
DTSTART:20210302T153000Z
DTEND:20210302T163000Z
DTSTAMP:20260422T225928Z
UID:OxfordRMT/16
DESCRIPTION:Title: The stochastic Airy operator and an interesting eigenvalue process\
nby Diane Holcomb (KTH Stockholm) as part of Oxford Random Matrix Theory S
eminars\n\n\nAbstract\nThe Gaussian ensembles\, originally introduced by W
igner may be generalized to an n-point ensemble called the beta-Hermite en
semble. As with the original ensembles we are interested in studying the l
ocal behavior of the eigenvalues. At the edges of the ensemble the rescale
d eigenvalues converge to the Airy_beta process which for general beta is
characterized as the eigenvalues of a certain random differential operator
called the stochastic Airy operator (SAO). In this talk I will give a sho
rt introduction to the Stochastic Airy Operator and the proof of convergen
ce of the eigenvalues\, before introducing another interesting eigenvalue
process. This process can be characterized as a limit of eigenvalues of mi
nors of the tridiagonal matrix model associated to the beta-Hermite ensemb
le as well as the process formed by the eigenvalues of the SAO under a res
triction of the domain. This is joint work with Angelica Gonzalez.\n
LOCATION:https://researchseminars.org/talk/OxfordRMT/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gernot Akemann (Universität Bielefeld)
DTSTART:20210309T153000Z
DTEND:20210309T163000Z
DTSTAMP:20260422T225928Z
UID:OxfordRMT/17
DESCRIPTION:Title: Territorial behaviour of buzzards and the 2D Coulomb gas\nby Gernot
Akemann (Universität Bielefeld) as part of Oxford Random Matrix Theory S
eminars\n\n\nAbstract\nNon-Hermitian random matrices with complex eigenval
ues represent a truly two-dimensional (2D) Coulomb gas at inverse temperat
ure beta=2. Compared to their Hermitian counter-parts they enjoy an enlarg
ed bulk and edge universality. As an application to ecology we model large
scale data of the approximately 2D distribution of buzzard nests in the T
eutoburger forest observed over a period of 20 y. These birds of prey show
a highly territorial behaviour. Their occupied nests are monitored annual
ly and we compare these data with a one-component 2D Coulomb gas of repell
ing charges as a function of beta. The nearest neighbour spacing distribut
ion of the nests is well described by fitting to beta as an effective repu
lsion parameter\, that lies between the universal predictions of Poisson (
beta=0) and random matrix statistics (beta=2). Using a time moving average
and comparing with next-to-nearest neighbours we examine the effect of a
population increase on beta and correlation length.\n
LOCATION:https://researchseminars.org/talk/OxfordRMT/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arno Kuijlaars (KU Leuven)
DTSTART:20210427T143000Z
DTEND:20210427T153000Z
DTSTAMP:20260422T225928Z
UID:OxfordRMT/18
DESCRIPTION:Title: The two-periodic Aztec diamond and matrix valued orthogonality\nby
Arno Kuijlaars (KU Leuven) as part of Oxford Random Matrix Theory Seminars
\n\n\nAbstract\nI will discuss how polynomials with a non-hermitian orthog
onality on a contour in the complex plane arise in certain random tiling p
roblems. In the case of periodic weightings the orthogonality is matrixval
ued.\n\nIn work with Maurice Duits (KTH Stockholm) the Riemann-Hilbert pro
blem for matrix valued orthogonal polynomials was used to obtain asymptoti
cs for domino tilings of the two-periodic Aztec diamond. This model is rem
arkable since it gives rise to a gaseous phase\, in addition to the more c
ommon solid and liquid phases.\n
LOCATION:https://researchseminars.org/talk/OxfordRMT/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Liza Rebrova (Lawrence Berkeley National Lab)
DTSTART:20210504T143000Z
DTEND:20210504T153000Z
DTSTAMP:20260422T225928Z
UID:OxfordRMT/19
DESCRIPTION:Title: On the iterative methods for corrupted linear systems\nby Liza Rebr
ova (Lawrence Berkeley National Lab) as part of Oxford Random Matrix Theor
y Seminars\n\n\nAbstract\nA group of projection based approaches for solvi
ng large-scale linear systems is known for its speed and simplicity. For e
xample\, Kaczmarz algorithm iteratively projects the previous approximatio
n x_k onto the solution spaces of the next equation in the system. An eleg
ant proof of the exponential convergence of this method\, using correct ra
ndomization of the process\, was given in 2009 by Strohmer and Vershynin\,
and succeeded by many extensions and generalizations. I will discuss our
newly developed variants of these methods that successfully avoid large an
d potentially adversarial corruptions in the linear system. I specifically
focus on the random matrix and high-dimensional probability results that
play a crucial role in proving convergence of such methods. Based on the j
oint work with Jamie Haddock\, Deanna Needell\, and Will Swartworth.\n
LOCATION:https://researchseminars.org/talk/OxfordRMT/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boris Khoruzhenko (Queen Mary University London)
DTSTART:20210511T143000Z
DTEND:20210511T153000Z
DTSTAMP:20260422T225928Z
UID:OxfordRMT/20
DESCRIPTION:Title: How many stable equilibria will a large complex system have?\nby Bo
ris Khoruzhenko (Queen Mary University London) as part of Oxford Random Ma
trix Theory Seminars\n\n\nAbstract\nIn 1972 Robert May argued that (generi
c) complex systems become unstable to small displacements from equilibria
as the system complexity increases. His analytical model and outlook was l
inear. I will talk about a “minimal” non-linear extension of May’s m
odel – a nonlinear autonomous system of N ≫ 1 degrees of freedom rando
mly coupled by both relaxational (’gradient’) and non-relaxational (
’solenoidal’) random interactions. With the increasing interaction str
ength such systems undergo an abrupt transition from a trivial phase portr
ait with a single stable equilibrium into a topologically non-trivial regi
me where equilibria are on average exponentially abundant\, but typically
all of them are unstable\, unless the dynamics is purely gradient. When th
e interaction strength increases even further the stable equilibria eventu
ally become on average exponentially abundant unless the interaction is pu
rely solenoidal. One can investigate these transitions with the help of th
e Kac-Rice formula for counting zeros of random functions and theory of ra
ndom matrices applied to the real elliptic ensemble with some of the mathe
matical problems remaining open. This talk is based on collaborative work
with Gerard Ben Arous and Yan Fyodorov.\n
LOCATION:https://researchseminars.org/talk/OxfordRMT/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maurice Duits (KTH Stockholm)
DTSTART:20210518T143000Z
DTEND:20210518T153000Z
DTSTAMP:20260422T225928Z
UID:OxfordRMT/21
DESCRIPTION:Title: Integrability of random tilings with doubly periodic weights\nby Ma
urice Duits (KTH Stockholm) as part of Oxford Random Matrix Theory Seminar
s\n\n\nAbstract\nIn recent years important progress has been made in the u
nderstanding of random tilings of large Aztec diamonds with doubly periodi
c weights. Due to the double periodicity a new phase appears that has not
been observed in tiling models with uniform weights. One of the challenge
s is to find expressions of for the correlation functions that are amenabl
e for asymptotic studies. In the case of the uniform weight the model is a
n example of a Schur process and\, consequently\, such expressions for th
e correlation functions are known and well-studied in that case. In a join
t work with Tomas Berggren we studied a more general integrable structur
e that includes certain doubly periodic weightings planar domains\, such a
s the Aztec diamond. A key feature is a dynamical system hiding in the ba
ckground. In case of a periodic orbit\, explicit double integrals for the
correlation function can be found\, paving the way for an asymptotic study
using saddle point methods.\n
LOCATION:https://researchseminars.org/talk/OxfordRMT/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mo Dick Wong (University of Oxford)
DTSTART:20210525T143000Z
DTEND:20210525T153000Z
DTSTAMP:20260422T225928Z
UID:OxfordRMT/22
DESCRIPTION:Title: There has been a lot of interest in recent years in understanding the m
ultifractality of characteristic polynomials of random matrices. In this t
alk I shall consider the study of moments of moments from the probabilisti
c perspective of Gaussian multiplicat\nby Mo Dick Wong (University of
Oxford) as part of Oxford Random Matrix Theory Seminars\n\n\nAbstract\nThe
re has been a lot of interest in recent years in understanding the multifr
actality of characteristic polynomials of random matrices. In this talk I
shall consider the study of moments of moments from the probabilistic pers
pective of Gaussian multiplicative chaos\, and in particular establish exa
ct asymptotics for the so-called critical-subcritical regime in the contex
t of large Haar-distributed unitary matrices. This is based on a joint wor
k with Jon Keating.\n
LOCATION:https://researchseminars.org/talk/OxfordRMT/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Konstantin Tikhomirov (Georgia Institute of Technology)
DTSTART:20210601T130000Z
DTEND:20210601T140000Z
DTSTAMP:20260422T225928Z
UID:OxfordRMT/23
DESCRIPTION:Title: Invertibility of random square matrices\nby Konstantin Tikhomirov (
Georgia Institute of Technology) as part of Oxford Random Matrix Theory Se
minars\n\n\nAbstract\nConsider an n by n random matrix A with i.i.d entrie
s. In this talk\, we discuss some results on the magnitude of the smallest
singular value of A\, and\, in particular\, the problem of estimating the
singularity probability when the entries of A are discrete.\n
LOCATION:https://researchseminars.org/talk/OxfordRMT/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jon Pitchford (University of York)
DTSTART:20210615T143000Z
DTEND:20210615T153000Z
DTSTAMP:20260422T225928Z
UID:OxfordRMT/24
DESCRIPTION:Title: Are random matrix models useful in biological systems?\nby Jon Pitc
hford (University of York) as part of Oxford Random Matrix Theory Seminars
\n\n\nAbstract\nFor five decades\, mathematicians have exploited the beaut
ies of random matrix theory (RMT) in the hope of discovering principles wh
ich govern complex ecosystems. While RMT lies at the heart of the ideas\,
their translation toward biological reality requires some heavy lifting: d
ynamical systems theory\, statistics\, and large-scale computations are in
volved\, and any predictions should be challenged with empirical data. Thi
s can become very awkward.\n\nIn addition to a morose journey through some
of my personal failures to make RMT meet reality\, I will try to sketch o
ut some more constructive future perspectives. In particular\, new methods
for microbial community composition\, dynamics and evolution might allow
us to apply RMT ideas to the treatment of cystic fibrosis. In addition\, i
n fisheries I will argue that sometimes the very absence of an empirical d
ataset can add to the practical value of models as tools to influence poli
cy.\n
LOCATION:https://researchseminars.org/talk/OxfordRMT/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gérard Ben Arous (New York University)
DTSTART:20210601T143000Z
DTEND:20210601T153000Z
DTSTAMP:20260422T225928Z
UID:OxfordRMT/25
DESCRIPTION:Title: Random Determinants and the Elastic Manifold\nby Gérard Ben Arous
(New York University) as part of Oxford Random Matrix Theory Seminars\n\n\
nAbstract\nThis is joint work with Paul Bourgade and Benjamin McKenna (Cou
rant Institute\, NYU).\n\nThe elastic manifold is a paradigmatic represent
ative of the class of disordered elastic systems. These models describe ra
ndom surfaces with rugged shapes resulting from a competition between rand
om spatial impurities (preferring disordered configurations)\, on the one
hand\, and elastic self-interactions (preferring ordered configurations)\,
on the other. The elastic manifold model is interesting because it displa
ys a depinning phase transition and has a long history as a testing ground
for new approaches in statistical physics of disordered media\, for examp
le for fixed dimension by Fisher (1986) using functional renormalization g
roup methods\, and in the high-dimensional limit by Mézard and Parisi (1
992) using the replica method. \n\nWe study the topology of the energy lan
dscape of this model in the Mézard-Parisi setting\, and compute the (anne
aled) topological complexity both of total critical points and of local mi
nima. Our main result confirms the recent formulas by Fyodorov and Le Dous
sal (2020) and allows to identify the boundary between simple and glassy p
hases. The core argument relies on the analysis of the asymptotic behavior
of large random determinants in the exponential scale.\n
LOCATION:https://researchseminars.org/talk/OxfordRMT/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alan Edelman (MIT)
DTSTART:20210610T130000Z
DTEND:20210610T140000Z
DTSTAMP:20260422T225928Z
UID:OxfordRMT/26
DESCRIPTION:Title: 53 Matrix Factorizations\, generalized Cartan\, and Random Matrix Theor
y\nby Alan Edelman (MIT) as part of Oxford Random Matrix Theory Semina
rs\n\n\nAbstract\nAn insightful exercise might be to ask what is the most
important idea in linear algebra. Our first answer would not be eigenvalue
s or linearity\, it would be “matrix factorizations.” We will discuss
a blueprint to generate 53 inter-related matrix factorizations (times 2)
most of which appear to be new. The underlying mathematics may be traced
back to Cartan (1927)\, Harish-Chandra (1956)\, and Flensted-Jensen (1978)
. We will discuss the interesting history. One anecdote is that Eugene Wi
gner (1968) discovered factorizations such as the svd in passing in a way
that was buried and only eight authors have referenced that work. Ironical
ly Wigner referenced Sigurður Helgason (1962) but Wigner did not recogniz
e his results in Helgason's book. This work also extends upon and complete
s open problems posed by Mackey²&Tisseur (2003/2005).\n\nClassical result
s of Random Matrix Theory concern exact formulas from the Hermite\, Laguer
re\, Jacobi\, and Circular distributions. Following an insight from Freema
n Dyson (1970)\, Zirnbauer (1996) and Duenez (2004/5) linked some of these
classical ensembles to Cartan's theory of Symmetric Spaces. One troubling
fact is that symmetric spaces alone do not cover all of the Jacobi ensemb
les. We present a completed theory based on the generalized Cartan distrib
ution. Furthermore\, we show how the matrix factorization obtained by the
generalized Cartan decomposition G=K₁AK₂ plays a crucial role in sampl
ing algorithms and the derivation of the joint probability density of A.\n
\nJoint work with Sungwoo Jeong.\n
LOCATION:https://researchseminars.org/talk/OxfordRMT/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandra Florea (UCI)
DTSTART:20211130T153000Z
DTEND:20211130T163000Z
DTSTAMP:20260422T225928Z
UID:OxfordRMT/27
DESCRIPTION:Title: The Ratios Conjecture over function fields\nby Alexandra Florea (UC
I) as part of Oxford Random Matrix Theory Seminars\n\n\nAbstract\nI will t
alk about some recent joint work with H. Bui and J. Keating where we study
the Ratios Conjecture for the family of quadratic L-functions over functi
on fields. I will also discuss the closely related problem of obtaining up
per bounds for negative moments of L-functions\, which allows us to obtain
partial results towards the Ratios Conjecture in the case of one over one
\, two over two and three over three L-functions.\n
LOCATION:https://researchseminars.org/talk/OxfordRMT/27/
END:VEVENT
END:VCALENDAR