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BEGIN:VEVENT
SUMMARY:Ofer Zeitouni (Weizmann Institute of Science)
DTSTART;VALUE=DATE-TIME:20200420T113000Z
DTEND;VALUE=DATE-TIME:20200420T123000Z
DTSTAMP;VALUE=DATE-TIME:20240329T023456Z
UID:HSPETDS/1
DESCRIPTION:Title:
Stability and instability of spectrum for noisy perturbations of non-Hermi
tian matrices\nby Ofer Zeitouni (Weizmann Institute of Science) as par
t of Horowitz seminar on probability\, ergodic theory and dynamical system
s\n\nLecture held in 309.\n\nAbstract\nWe discuss the spectrum of high dim
ensional non-Hermitian matrices under small noisy perturbations. That spec
trum can be extremely unstable\, as the maximal nilpotent matrix JN with J
N(i\,j)=1 iff j=i+1 demonstrates. Numerical analysts studied worst case pe
rturbations\, using the notion of pseudo-spectrum. Our focus is on finding
the locus of most eigenvalues (limits of density of states)\, as well as
studying stray eigenvalues ("outliers"). I will describe the background\,
show some fun and intriguing simulations\, and present some theorems and w
ork in progress concerning eigenvectors. No background will be assumed. Th
e talk is based on joint work with Anirban Basak\, Elliot Paquette\, and M
artin Vogel.\n
LOCATION:https://researchseminars.org/talk/HSPETDS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tal Orenshtein (TU Berlin\, Weierstrass Institute and Free Univers
ity of Berlin)
DTSTART;VALUE=DATE-TIME:20200427T113000Z
DTEND;VALUE=DATE-TIME:20200427T123000Z
DTSTAMP;VALUE=DATE-TIME:20240329T023456Z
UID:HSPETDS/2
DESCRIPTION:Title:
Rough walks in random environment\nby Tal Orenshtein (TU Berlin\, Weie
rstrass Institute and Free University of Berlin) as part of Horowitz semin
ar on probability\, ergodic theory and dynamical systems\n\nLecture held i
n 309.\n\nAbstract\nRandom walks in random environment have been extensive
ly studied in the last half-century and invariance principles are known to
hold in various cases. We shall discuss recent contributions\, where the
scaling limit is obtained in the rough path space for the lifted random wa
lk. Except for the immediate application to stochastic differential equati
ons\, this provides new information on the structure of the limiting path
- an enhanced Brownian motion with a linearly perturbed second level\, whi
ch is characterized in various ways. Time permitting\, we shall elaborate
on the main tools to tackle these problems. Based on joint works with Olga
Lopusanschi\, with Jean-Dominique Deuschel and Nicolas Perkowski and with
Johaness Bäumler\, Noam Berger and Martin Slowik.\n
LOCATION:https://researchseminars.org/talk/HSPETDS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christophe Garban (Université Lyon 1)
DTSTART;VALUE=DATE-TIME:20200504T113000Z
DTEND;VALUE=DATE-TIME:20200504T123000Z
DTSTAMP;VALUE=DATE-TIME:20240329T023456Z
UID:HSPETDS/4
DESCRIPTION:Title:
Kosterlitz-Thouless transition and statistical reconstruction of the Gauss
ian free field\nby Christophe Garban (Université Lyon 1) as part of H
orowitz seminar on probability\, ergodic theory and dynamical systems\n\nL
ecture held in 309.\n\nAbstract\nThe Berezinskii-Kosterlitz-Thouless trans
ition (BKT transition) is a phase transition which occurs in dimension two
for spin systems such as the plane rotator model (or XY model). This phas
e transition was discovered by these three physicists as the first example
of a topological phase transition and was rigorously understood by Fröhl
ich and Spencer in the 80's. I will spend the main part of my talk explain
ing what are these topological phase transitions. I will then survey the c
ontributions of Fröhlich and Spencer to this theory and I will end with n
ew results we obtained recently with Avelio Sepúlveda in this direction.\
nThe talk will be based mostly on the preprint: https://arxiv.org/abs/2002
.12284\n
LOCATION:https://researchseminars.org/talk/HSPETDS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Renan Gross (Weizmann Institute)
DTSTART;VALUE=DATE-TIME:20200511T113000Z
DTEND;VALUE=DATE-TIME:20200511T123000Z
DTSTAMP;VALUE=DATE-TIME:20240329T023456Z
UID:HSPETDS/5
DESCRIPTION:Title:
Stochastic processes for Boolean profit\nby Renan Gross (Weizmann Inst
itute) as part of Horowitz seminar on probability\, ergodic theory and dyn
amical systems\n\nLecture held in 309.\n\nAbstract\nNot even influence ine
qualities for Boolean functions can escape the long arm of stochastic proc
esses. I will present a (relatively) natural stochastic process which turn
s Boolean functions and their derivatives into jump-process martingales. T
here is much to profit from analyzing the individual paths of these proces
ses: Using stopping times and level inequalities\, we will prove a conject
ure of Talagrand relating edge boundaries and the influences\, and show st
ability of KKL\, isoperimetric\, and Talagrand's influence inequality. The
technique (mostly) bypasses hypercontractivity. Work with Ronen Eldan.\n
LOCATION:https://researchseminars.org/talk/HSPETDS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Izabella Stuhl (Penn State University)
DTSTART;VALUE=DATE-TIME:20200518T120000Z
DTEND;VALUE=DATE-TIME:20200518T130000Z
DTSTAMP;VALUE=DATE-TIME:20240329T023456Z
UID:HSPETDS/6
DESCRIPTION:Title:
The hard-core model in discrete 2D\nby Izabella Stuhl (Penn State Univ
ersity) as part of Horowitz seminar on probability\, ergodic theory and dy
namical systems\n\n\nAbstract\nThe hard-core model describes a system of n
on-overlapping identical hard spheres in a space or on a lattice (more gen
erally\, on a graph). An interesting open problem is: do hard disks in a p
lane admit a unique Gibbs measure at high density? It seems natural to app
roach this question by possible discrete approximations where disks must h
ave the centers at sites of a lattice or vertices of a graph.\n\nIn this t
alk\, I will report on progress achieved for the models on a unit triangul
ar lattice $\\mathbb{A}_2$\, square lattice $\\mathbb{Z}^2$ and a honeycom
b graph $\\mathbb{H}_2$ for a general value of disk diameter $D$ (in the E
uclidean metric). We analyze the structure of Gibbs measures for large fug
acities (i.e.\, high densities) by means of the Pirogov-Sinai theory and i
ts modifications. It connects extreme Gibbs measures with dominant ground
states.\n\nOn $\\mathbb{A}_2$ we give a complete description of the set of
extreme Gibbs measures\; the answer is provided in terms of the prime dec
omposition of the Löschian number $D^2$ in the Eisenstein integer ring. O
n $\\mathbb{Z}^2$\, we work with Gaussian numbers. Here we have to exclude
a finite collection of values of $D$ with sliding\; for the remaining exc
lusion distances the answer is given in terms of solutions to a discrete m
inimization problem. The latter is connected to norm equations in the cycl
otomic integer ring $\\mathbb{Z}[\\zeta]$\, where $\\zeta$ is a primitive
12th root of unity. On $\\mathbb{H}_2$\, we employ connections with the mo
del on $\\mathbb{A}_2$\, although there are some exceptional values requir
ing a special approach.\n\nParts of our argument contain computer-assisted
proofs: identification of instances of sliding\, resolution of dominance
issues. This is a joint work with A. Mazel and Y. Suhov.\n
LOCATION:https://researchseminars.org/talk/HSPETDS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Dario (Tel Aviv University)
DTSTART;VALUE=DATE-TIME:20200525T120000Z
DTEND;VALUE=DATE-TIME:20200525T130000Z
DTSTAMP;VALUE=DATE-TIME:20240329T023456Z
UID:HSPETDS/7
DESCRIPTION:Title:
Large-scale behavior of the Villain model at low temperature in d = 3\
nby Paul Dario (Tel Aviv University) as part of Horowitz seminar on probab
ility\, ergodic theory and dynamical systems\n\n\nAbstract\nIn this talk\,
we will study the Villain rotator model in dimension three and prove that
\, at low temperature\, the truncated two-point function of the model deca
ys asymptotically like $|x|^{2-d}$\, with an algebraic rate of convergence
. The argument starts from the observation that the asymptotic properties
of the Villain model are related to the large-scale behavior of a vector-v
alued random surface with uniformly elliptic and infinite range potential\
, following the arguments of Fröhlich\, Spencer and Bauerschmidt. We will
then see that this behavior can be studied quantitatively by combining tw
o sets of tools: the Helffer-Sjöstrand PDE\, initially introduced by Nadd
af and Spencer to identify the scaling limit of the discrete Ginzburg-Land
au model\, and the techniques of the quantitative theory of stochastic hom
ogenization developed by Armstrong\, Kuusi and Mourrat. Joint work with We
i Wu.\n
LOCATION:https://researchseminars.org/talk/HSPETDS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ofir Gorodetsky (Tel Aviv University)
DTSTART;VALUE=DATE-TIME:20200316T123000Z
DTEND;VALUE=DATE-TIME:20200316T133000Z
DTSTAMP;VALUE=DATE-TIME:20240329T023456Z
UID:HSPETDS/9
DESCRIPTION:Title:
The anatomy of integers and Ewens permutations\nby Ofir Gorodetsky (Te
l Aviv University) as part of Horowitz seminar on probability\, ergodic th
eory and dynamical systems\n\n\nAbstract\nWe will discuss an analogy betwe
en integers and permutations\, an analogy which goes back to works of Erd
ős and Kac and of Billingsley which we shall survey. Certain statistics o
f the prime factors of a uniformly drawn integer (between $1$ and $x$) agr
ee\, in the limit\, with similar statistics of the cycles of a uniformly d
rawn permutation from the symmetric group on $n$ elements. This analogy is
beneficial to both number theory and probability theory\, as one can ofte
n prove new number-theoretical results by employing probabilistic ideas\,
and vice versa.\nThe Ewens measure with parameter Θ\, first discovered in
the context of population genetics\, is a non-uniform measure on permutat
ions. We will present an analogue of this measure on the integers\, and sh
ow how natural questions on the integers have answers which agree with ana
logous problems for the Ewens measure. For example\, the size of the prime
factors of integers which are sums of two squares\, and the cycle lengths
of permutations drawn according to the Ewens measure with parameter 1/2\,
both converge to the Poisson-Dirichlet process with parameter 1/2. We wil
l convey some of the ideas behind the proofs.\nJoint work with Dor Elboim.
\n
LOCATION:https://researchseminars.org/talk/HSPETDS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matan Seidel (Tel Aviv University)
DTSTART;VALUE=DATE-TIME:20200323T123000Z
DTEND;VALUE=DATE-TIME:20200323T133000Z
DTSTAMP;VALUE=DATE-TIME:20240329T023456Z
UID:HSPETDS/10
DESCRIPTION:Title: Random walks on circle packings\nby Matan Seidel (Tel Aviv University
) as part of Horowitz seminar on probability\, ergodic theory and dynamica
l systems\n\n\nAbstract\nA circle packing is a canonical way of representi
ng a planar graph. There is a deep connection between the geometry of the
circle packing and the probabilistic property of recurrence/transience of
the simple random walk on the underlying graph\, as shown in the famous He
-Schramm Theorem. The removal of one of the Theorem's assumptions - that o
f bounded degrees - can cause the theorem to fail. However\, by using cert
ain natural weights that arise from the circle packing for a weighted rand
om walk\, (at least) one of the directions of the He-Schramm Theorem remai
ns true. In the talk I will present some of the theory of circle packings
and random walks and discuss some of the ideas used in the proof. Joint wo
rk with Ori Gurel-Gurevich.\n
LOCATION:https://researchseminars.org/talk/HSPETDS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nathanaël Berestycki (University of Vienna)
DTSTART;VALUE=DATE-TIME:20200330T113000Z
DTEND;VALUE=DATE-TIME:20200330T123000Z
DTSTAMP;VALUE=DATE-TIME:20240329T023456Z
UID:HSPETDS/11
DESCRIPTION:Title: Random walks on random planar maps and Liouville Brownian motion\nby
Nathanaël Berestycki (University of Vienna) as part of Horowitz seminar o
n probability\, ergodic theory and dynamical systems\n\n\nAbstract\nThe st
udy of random walks on random planar maps was initiated in a series of sem
inal papers of Benjamini and Schramm at the end of the 90s\, motivated by
contemporary (nonrigourous) works in the study of Liouville Quantum Gravit
y (LQG). Both topics have been the subject of intense research following r
emarkable breakthroughs in the last few years.\n\nAfter reviewing some of
the recent developments in these fields - including Liouville Brownian mot
ion\, a canonical notion of diffusion on LQG surfaces - I will describe so
me joint work with Ewain Gwynne. In this work we show that random walks on
certain models of random planar maps (known as mated-CRT planar maps) hav
e a scaling limit given by Liouville Brownian motion. This is true whether
the maps are embedded using SLE/LQG theory or more intrinsically using th
e Tutte embedding. This is the first result confirming that Liouville Brow
nian motion is the scaling limit of random walks on random planar maps.\n\
nThe proof relies on some earlier work of Gwynne\, Miller and Sheffield wh
ich proves convergence to Brownian motion\, modulo time-parametrisation. A
s an intermediate result of independent interest\, we derive an axiomatic
characterisation of Liouville Brownian motion\, for which the notion of Re
vuz measure of a Markov process plays a crucial role.\n
LOCATION:https://researchseminars.org/talk/HSPETDS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Chelkak (École Normale Supérieure Paris and St. Petersbur
g Dept. of Steklov Institute RAS)
DTSTART;VALUE=DATE-TIME:20200601T120000Z
DTEND;VALUE=DATE-TIME:20200601T130000Z
DTSTAMP;VALUE=DATE-TIME:20240329T023456Z
UID:HSPETDS/12
DESCRIPTION:Title: Bipartite dimer model: Gaussian Free Field on Lorentz-minimal surfaces\nby Dmitry Chelkak (École Normale Supérieure Paris and St. Petersburg
Dept. of Steklov Institute RAS) as part of Horowitz seminar on probability
\, ergodic theory and dynamical systems\n\n\nAbstract\nWe discuss a new vi
ewpoint on the convergence of fluctuations in the bipartite dimer model co
nsidered on big planar graphs. Classically\, when these graphs are parts o
f refining lattices\, the boundary profile of the height function and a la
ttice-dependent entropy functional are responsible for the conformal struc
ture\, in which the limiting GFF (and CLE(4)) should be defined. Motivated
by a long-term perspective of understanding the `discrete conformal struc
ture’ of random planar maps equipped with the dimer (or the critical Isi
ng) model\, we introduce `perfect t-embeddings’ of abstract weighted bip
artite graphs and argue that such embeddings reveal the conformal structur
e in a universal way: as that of a related Lorentz-minimal surface in 2+1
(or 2+2) dimensions.\n\nThough the whole concept is very new\, concrete de
terministic examples (e.g\, the Aztec diamond) justify its relevance\, and
general convergence theorems obtained so far are of their own interest. S
till\, many open questions remain\, one of the key ones being to understan
d the mechanism behind the appearance of the Lorentz metric in this classi
cal problem.\n\nBased upon recent joint works with Benoît Laslier\, Sanja
y Ramassamy and Marianna Russkikh.\n
LOCATION:https://researchseminars.org/talk/HSPETDS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thierry Bodineau (École Polytechnique)
DTSTART;VALUE=DATE-TIME:20200608T120000Z
DTEND;VALUE=DATE-TIME:20200608T130000Z
DTSTAMP;VALUE=DATE-TIME:20240329T023456Z
UID:HSPETDS/13
DESCRIPTION:Title: Fluctuating Boltzmann equation and large deviations for a hard sphere gas
\nby Thierry Bodineau (École Polytechnique) as part of Horowitz semin
ar on probability\, ergodic theory and dynamical systems\n\n\nAbstract\nSi
nce the seminal work of Lanford\, the convergence of the hard-sphere dynam
ics towards the Boltzmann equation has been established in a dilute gas as
ymptotic. In this talk\, we are going to discuss the fluctuations of this
microscopic dynamics around the Boltzmann equation and the convergence of
the fluctuation field to a generalised Ornstein-Uhlenbeck process. We will
show also that the occurrence of atypical evolutions can be quantified by
a large deviation principle. This analysis relies on the study of the cor
relations created by the Hamiltonian dynamics. We will see that the emerge
nce of irreversibility in the kinetic limit can be related to the singular
ity of these correlations.\n
LOCATION:https://researchseminars.org/talk/HSPETDS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Osama Khalil (University of Utah)
DTSTART;VALUE=DATE-TIME:20200615T140000Z
DTEND;VALUE=DATE-TIME:20200615T150000Z
DTSTAMP;VALUE=DATE-TIME:20240329T023456Z
UID:HSPETDS/14
DESCRIPTION:Title: Singular Vectors on Fractals and Homogeneous Flows\nby Osama Khalil (
University of Utah) as part of Horowitz seminar on probability\, ergodic t
heory and dynamical systems\n\n\nAbstract\nThe theory of Diophantine appro
ximation is underpinned by Dirichlet’s fundamental theorem. Broadly spea
king\, the main questions in the theory concern quantifying the prevalence
of points with exceptional behavior with respect to Dirichlet’s result.
The work of Dani and Kleinbock-Margulis connects these questions to the r
ecurrence behavior of certain flows on homogeneous spaces. For example\, d
ivergent orbits of such flows correspond to so-called singular vectors. Af
ter a brief overview of the subject and the motivating questions\, I will
discuss new results giving a sharp upper bound on the Hausdorff dimension
of divergent orbits of certain diagonal flows emanating from fractals on t
he space of unimodular lattices. Time permitting\, connections to the theo
ry of projections of self-similar measures will be presented.\n
LOCATION:https://researchseminars.org/talk/HSPETDS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tyler Helmuth (University of Bristol)
DTSTART;VALUE=DATE-TIME:20200622T120000Z
DTEND;VALUE=DATE-TIME:20200622T130000Z
DTSTAMP;VALUE=DATE-TIME:20240329T023456Z
UID:HSPETDS/15
DESCRIPTION:Title: Random spanning forests and hyperbolic symmetry\nby Tyler Helmuth (Un
iversity of Bristol) as part of Horowitz seminar on probability\, ergodic
theory and dynamical systems\n\n\nAbstract\nThe arboreal gas is the probab
ility measure that arises from conditioning the random subgraph given by B
ernoulli($p$) bond percolation to be a spanning forest\, i.e.\, to contain
no cycles. This conditioning makes sense on any finite graph $G$\, and in
the case $p=1/2$ gives the uniform measure on spanning forests. The arbor
eal gas also arises as a $q\\to0$ limit of the $q$-state random cluster mo
del.\n\nWhat are the percolative properties of these forests? This turns o
ut to be a surprisingly rich question\, and I will discuss what is known a
nd conjectured. I will also describe a tool for studying connection probab
ilities\, the magic formula\, which arises due to an important connection
between the arboreal gas and spin systems with hyperbolic symmetry.\n\nBas
ed on joint work with Roland Bauerschmidt\, Nick Crawford\, and Andrew Swa
n.\n
LOCATION:https://researchseminars.org/talk/HSPETDS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yaar Solomon (Ben-Gurion university of the Negev)
DTSTART;VALUE=DATE-TIME:20200629T120000Z
DTEND;VALUE=DATE-TIME:20200629T130000Z
DTSTAMP;VALUE=DATE-TIME:20240329T023456Z
UID:HSPETDS/16
DESCRIPTION:Title: Bounded-displacement non-equivalence in substitution tilings\nby Yaar
Solomon (Ben-Gurion university of the Negev) as part of Horowitz seminar
on probability\, ergodic theory and dynamical systems\n\n\nAbstract\nGiven
two Delone sets $Y$ and $Z$ in $R^d$ we study the existence of a bounded-
displacement (BD) map between them\, namely a bijection $f$ from $Y$ to $Z
$ so that the quantity $\\|y-f(y)\\|$\, $y\\in Y$\, is bounded. This notio
n induces an equivalence relation on collections $X$ of Delone sets and we
study the cardinality of BD($X$)\, a collection of all BD-class represent
atives. In this talk we focus on sets $X$ of point sets that correspond to
tilings in a substitution tiling space. We provide a sufficient condition
under which |BD($X$)| is the continuum. In particular we show that\, in t
he context of primitive substitution tilings\, |BD($X$)| can be greater th
an $1$.\n
LOCATION:https://researchseminars.org/talk/HSPETDS/16/
END:VEVENT
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