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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:20201029T110621Z
UID:HSPETDS/1
DESCRIPTION:Title: Stability and instability of spectrum for noisy perturb
ations of non-Hermitian matrices\nby Ofer Zeitouni (Weizmann Institute of
Science) as part of Horowitz seminar on probability\, ergodic theory and d
ynamical systems\n\nLecture held in 309.\n\nAbstract\nWe discuss the spect
rum of high dimensional non-Hermitian matrices under small noisy perturbat
ions. That spectrum can be extremely unstable\, as the maximal nilpotent m
atrix JN with JN(i\,j)=1 iff j=i+1 demonstrates. Numerical analysts studie
d worst case perturbations\, using the notion of pseudo-spectrum. Our focu
s is on finding the locus of most eigenvalues (limits of density of states
)\, as well as studying stray eigenvalues ("outliers"). I will describe th
e background\, show some fun and intriguing simulations\, and present some
theorems and work in progress concerning eigenvectors. No background will
be assumed. The talk is based on joint work with Anirban Basak\, Elliot P
aquette\, and Martin Vogel.\n
LOCATION:Lecture held in 309
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:20201029T110621Z
UID:HSPETDS/2
DESCRIPTION:Title: Rough walks in random environment\nby Tal Orenshtein (T
U Berlin\, Weierstrass Institute and Free University of Berlin) as part of
Horowitz seminar on probability\, ergodic theory and dynamical systems\n\
nLecture held in 309.\n\nAbstract\nRandom walks in random environment have
been extensively studied in the last half-century and invariance principl
es are known to hold in various cases. We shall discuss recent contributio
ns\, where the scaling limit is obtained in the rough path space for the l
ifted random walk. Except for the immediate application to stochastic diff
erential equations\, this provides new information on the structure of the
limiting path - an enhanced Brownian motion with a linearly perturbed sec
ond level\, which is characterized in various ways. Time permitting\, we s
hall elaborate on the main tools to tackle these problems. Based on joint
works with Olga Lopusanschi\, with Jean-Dominique Deuschel and Nicolas Per
kowski and with Johaness Bäumler\, Noam Berger and Martin Slowik.\n
LOCATION:Lecture held in 309
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christophe Garban (Université Lyon 1)
DTSTART;VALUE=DATE-TIME:20200504T113000Z
DTEND;VALUE=DATE-TIME:20200504T123000Z
DTSTAMP;VALUE=DATE-TIME:20201029T110621Z
UID:HSPETDS/4
DESCRIPTION:Title: Kosterlitz-Thouless transition and statistical reconstr
uction of the Gaussian free field\nby Christophe Garban (Université Lyon
1) as part of Horowitz seminar on probability\, ergodic theory and dynamic
al systems\n\nLecture held in 309.\n\nAbstract\nThe Berezinskii-Kosterlitz
-Thouless transition (BKT transition) is a phase transition which occurs i
n dimension two for spin systems such as the plane rotator model (or XY mo
del). This phase transition was discovered by these three physicists as th
e first example of a topological phase transition and was rigorously under
stood by Fröhlich and Spencer in the 80's. I will spend the main part of
my talk explaining what are these topological phase transitions. I will th
en survey the contributions of Fröhlich and Spencer to this theory and I
will end with new results we obtained recently with Avelio Sepúlveda in t
his direction.\nThe talk will be based mostly on the preprint: https://arx
iv.org/abs/2002.12284\n
LOCATION:Lecture held in 309
END:VEVENT
BEGIN:VEVENT
SUMMARY:Renan Gross (Weizmann Institute)
DTSTART;VALUE=DATE-TIME:20200511T113000Z
DTEND;VALUE=DATE-TIME:20200511T123000Z
DTSTAMP;VALUE=DATE-TIME:20201029T110621Z
UID:HSPETDS/5
DESCRIPTION:Title: Stochastic processes for Boolean profit\nby Renan Gross
(Weizmann Institute) as part of Horowitz seminar on probability\, ergodic
theory and dynamical systems\n\nLecture held in 309.\n\nAbstract\nNot eve
n influence inequalities for Boolean functions can escape the long arm of
stochastic processes. I will present a (relatively) natural stochastic pro
cess which turns Boolean functions and their derivatives into jump-process
martingales. There is much to profit from analyzing the individual paths
of these processes: Using stopping times and level inequalities\, we will
prove a conjecture of Talagrand relating edge boundaries and the influence
s\, and show stability of KKL\, isoperimetric\, and Talagrand's influence
inequality. The technique (mostly) bypasses hypercontractivity. Work with
Ronen Eldan.\n
LOCATION:Lecture held in 309
END:VEVENT
BEGIN:VEVENT
SUMMARY:Izabella Stuhl (Penn State University)
DTSTART;VALUE=DATE-TIME:20200518T120000Z
DTEND;VALUE=DATE-TIME:20200518T130000Z
DTSTAMP;VALUE=DATE-TIME:20201029T110621Z
UID:HSPETDS/6
DESCRIPTION:Title: The hard-core model in discrete 2D\nby Izabella Stuhl (
Penn State University) as part of Horowitz seminar on probability\, ergodi
c theory and dynamical systems\n\n\nAbstract\nThe hard-core model describe
s a system of non-overlapping identical hard spheres in a space or on a la
ttice (more generally\, on a graph). An interesting open problem is: do ha
rd disks in a plane admit a unique Gibbs measure at high density? It seems
natural to approach this question by possible discrete approximations whe
re disks must have the centers at sites of a lattice or vertices of a grap
h.\n\nIn this talk\, I will report on progress achieved for the models on
a unit triangular lattice $\\mathbb{A}_2$\, square lattice $\\mathbb{Z}^2$
and a honeycomb graph $\\mathbb{H}_2$ for a general value of disk diamete
r $D$ (in the Euclidean metric). We analyze the structure of Gibbs measure
s for large fugacities (i.e.\, high densities) by means of the Pirogov-Sin
ai theory and its modifications. It connects extreme Gibbs measures with d
ominant ground states.\n\nOn $\\mathbb{A}_2$ we give a complete descriptio
n of the set of extreme Gibbs measures\; the answer is provided in terms o
f the prime decomposition of the Löschian number $D^2$ in the Eisenstein
integer ring. On $\\mathbb{Z}^2$\, we work with Gaussian numbers. Here we
have to exclude a finite collection of values of $D$ with sliding\; for th
e remaining exclusion distances the answer is given in terms of solutions
to a discrete minimization problem. The latter is connected to norm equati
ons in the cyclotomic integer ring $\\mathbb{Z}[\\zeta]$\, where $\\zeta$
is a primitive 12th root of unity. On $\\mathbb{H}_2$\, we employ connecti
ons with the model on $\\mathbb{A}_2$\, although there are some exceptiona
l values requiring a special approach.\n\nParts of our argument contain co
mputer-assisted proofs: identification of instances of sliding\, resolutio
n of dominance issues. This is a joint work with A. Mazel and Y. Suhov.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Dario (Tel Aviv University)
DTSTART;VALUE=DATE-TIME:20200525T120000Z
DTEND;VALUE=DATE-TIME:20200525T130000Z
DTSTAMP;VALUE=DATE-TIME:20201029T110621Z
UID:HSPETDS/7
DESCRIPTION:Title: Large-scale behavior of the Villain model at low temper
ature in d = 3\nby Paul Dario (Tel Aviv University) as part of Horowitz se
minar on probability\, 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 decays asymptotically like $|x|^{2-d}$\, with an algebraic rate
of convergence. The argument starts from the observation that the asympto
tic properties of the Villain model are related to the large-scale behavio
r of a vector-valued random surface with uniformly elliptic and infinite r
ange potential\, following the arguments of Fröhlich\, Spencer and Bauers
chmidt. We will then see that this behavior can be studied quantitatively
by combining two sets of tools: the Helffer-Sjöstrand PDE\, initially int
roduced by Naddaf and Spencer to identify the scaling limit of the discret
e Ginzburg-Landau model\, and the techniques of the quantitative theory of
stochastic homogenization developed by Armstrong\, Kuusi and Mourrat. Joi
nt work with Wei Wu.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ofir Gorodetsky (Tel Aviv University)
DTSTART;VALUE=DATE-TIME:20200316T123000Z
DTEND;VALUE=DATE-TIME:20200316T133000Z
DTSTAMP;VALUE=DATE-TIME:20201029T110621Z
UID:HSPETDS/9
DESCRIPTION:Title: The anatomy of integers and Ewens permutations\nby Ofir
Gorodetsky (Tel Aviv University) as part of Horowitz seminar on probabili
ty\, ergodic theory and dynamical systems\n\n\nAbstract\nWe will discuss a
n analogy between integers and permutations\, an analogy which goes back t
o works of Erdős and Kac and of Billingsley which we shall survey. Certai
n statistics of the prime factors of a uniformly drawn integer (between $1
$ and $x$) agree\, in the limit\, with similar statistics of the cycles of
a uniformly drawn permutation from the symmetric group on $n$ elements. T
his analogy is beneficial to both number theory and probability theory\, a
s one can often prove new number-theoretical results by employing probabil
istic ideas\, and vice versa.\nThe Ewens measure with parameter Θ\, first
discovered in the context of population genetics\, is a non-uniform measu
re on permutations. We will present an analogue of this measure on the int
egers\, and show how natural questions on the integers have answers which
agree with analogous problems for the Ewens measure. For example\, the siz
e 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 p
arameter 1/2\, both converge to the Poisson-Dirichlet process with paramet
er 1/2. We will convey some of the ideas behind the proofs.\nJoint work wi
th Dor Elboim.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matan Seidel (Tel Aviv University)
DTSTART;VALUE=DATE-TIME:20200323T123000Z
DTEND;VALUE=DATE-TIME:20200323T133000Z
DTSTAMP;VALUE=DATE-TIME:20201029T110621Z
UID:HSPETDS/10
DESCRIPTION:Title: Random walks on circle packings\nby Matan Seidel (Tel A
viv University) as part of Horowitz seminar on probability\, ergodic theor
y and dynamical systems\n\n\nAbstract\nA circle packing is a canonical way
of representing a planar graph. There is a deep connection between the ge
ometry 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 assump
tions - that of bounded degrees - can cause the theorem to fail. However\,
by using certain natural weights that arise from the circle packing for a
weighted random walk\, (at least) one of the directions of the He-Schramm
Theorem remains true. In the talk I will present some of the theory of ci
rcle packings and random walks and discuss some of the ideas used in the p
roof. Joint work with Ori Gurel-Gurevich.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nathanaël Berestycki (University of Vienna)
DTSTART;VALUE=DATE-TIME:20200330T113000Z
DTEND;VALUE=DATE-TIME:20200330T123000Z
DTSTAMP;VALUE=DATE-TIME:20201029T110621Z
UID:HSPETDS/11
DESCRIPTION:Title: Random walks on random planar maps and Liouville Browni
an motion\nby Nathanaël Berestycki (University of Vienna) as part of Horo
witz seminar on probability\, ergodic theory and dynamical systems\n\n\nAb
stract\nThe study of random walks on random planar maps was initiated in a
series of seminal papers of Benjamini and Schramm at the end of the 90s\,
motivated by contemporary (nonrigourous) works in the study of Liouville
Quantum Gravity (LQG). Both topics have been the subject of intense resear
ch following remarkable breakthroughs in the last few years.\n\nAfter revi
ewing some of the recent developments in these fields - including Liouvill
e Brownian motion\, a canonical notion of diffusion on LQG surfaces - I wi
ll describe some joint work with Ewain Gwynne. In this work we show that r
andom walks on certain models of random planar maps (known as mated-CRT pl
anar maps) have a scaling limit given by Liouville Brownian motion. This i
s true whether the maps are embedded using SLE/LQG theory or more intrinsi
cally using the Tutte embedding. This is the first result confirming that
Liouville Brownian motion is the scaling limit of random walks on random p
lanar maps.\n\nThe proof relies on some earlier work of Gwynne\, Miller an
d Sheffield which proves convergence to Brownian motion\, modulo time-para
metrisation. As an intermediate result of independent interest\, we derive
an axiomatic characterisation of Liouville Brownian motion\, for which th
e notion of Revuz measure of a Markov process plays a crucial role.\n
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:20201029T110621Z
UID:HSPETDS/12
DESCRIPTION:Title: Bipartite dimer model: Gaussian Free Field on Lorentz-m
inimal surfaces\nby Dmitry Chelkak (École Normale Supérieure Paris and S
t. Petersburg Dept. of Steklov Institute RAS) as part of Horowitz seminar
on probability\, ergodic theory and dynamical systems\n\n\nAbstract\nWe di
scuss a new viewpoint on the convergence of fluctuations in the bipartite
dimer model considered on big planar graphs. Classically\, when these grap
hs are parts of refining lattices\, the boundary profile of the height fun
ction and a lattice-dependent entropy functional are responsible for the c
onformal structure\, in which the limiting GFF (and CLE(4)) should be defi
ned. Motivated by a long-term perspective of understanding the `discrete c
onformal structure’ of random planar maps equipped with the dimer (or th
e critical Ising) model\, we introduce `perfect t-embeddings’ of abstrac
t weighted bipartite graphs and argue that such embeddings reveal the conf
ormal structure in a universal way: as that of a related Lorentz-minimal s
urface in 2+1 (or 2+2) dimensions.\n\nThough the whole concept is very new
\, concrete deterministic examples (e.g\, the Aztec diamond) justify its r
elevance\, and general convergence theorems obtained so far are of their o
wn interest. Still\, many open questions remain\, one of the key ones bein
g to understand the mechanism behind the appearance of the Lorentz metric
in this classical problem.\n\nBased upon recent joint works with Benoît L
aslier\, Sanjay Ramassamy and Marianna Russkikh.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thierry Bodineau (École Polytechnique)
DTSTART;VALUE=DATE-TIME:20200608T120000Z
DTEND;VALUE=DATE-TIME:20200608T130000Z
DTSTAMP;VALUE=DATE-TIME:20201029T110621Z
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 seminar on probability\, ergodic theory and dynamical systems\n\n
\nAbstract\nSince the seminal work of Lanford\, the convergence of the har
d-sphere dynamics towards the Boltzmann equation has been established in a
dilute gas asymptotic. In this talk\, we are going to discuss the fluctua
tions of this microscopic dynamics around the Boltzmann equation and the c
onvergence of the fluctuation field to a generalised Ornstein-Uhlenbeck pr
ocess. We will show also that the occurrence of atypical evolutions can be
quantified by a large deviation principle. This analysis relies on the st
udy of the correlations created by the Hamiltonian dynamics. We will see t
hat the emergence of irreversibility in the kinetic limit can be related t
o the singularity of these correlations.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Osama Khalil (University of Utah)
DTSTART;VALUE=DATE-TIME:20200615T140000Z
DTEND;VALUE=DATE-TIME:20200615T150000Z
DTSTAMP;VALUE=DATE-TIME:20201029T110621Z
UID:HSPETDS/14
DESCRIPTION:Title: Singular Vectors on Fractals and Homogeneous Flows\nby
Osama Khalil (University of Utah) as part of Horowitz seminar on probabili
ty\, ergodic theory and dynamical systems\n\n\nAbstract\nThe theory of Dio
phantine approximation is underpinned by Dirichlet’s fundamental theorem
. Broadly speaking\, the main questions in the theory concern quantifying
the prevalence of points with exceptional behavior with respect to Dirichl
et’s result. The work of Dani and Kleinbock-Margulis connects these ques
tions to the recurrence behavior of certain flows on homogeneous spaces. F
or example\, divergent orbits of such flows correspond to so-called singul
ar vectors. After a brief overview of the subject and the motivating quest
ions\, I will discuss new results giving a sharp upper bound on the Hausdo
rff dimension of divergent orbits of certain diagonal flows emanating from
fractals on the space of unimodular lattices. Time permitting\, connectio
ns to the theory of projections of self-similar measures will be presented
.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tyler Helmuth (University of Bristol)
DTSTART;VALUE=DATE-TIME:20200622T120000Z
DTEND;VALUE=DATE-TIME:20200622T130000Z
DTSTAMP;VALUE=DATE-TIME:20201029T110621Z
UID:HSPETDS/15
DESCRIPTION:Title: Random spanning forests and hyperbolic symmetry\nby Tyl
er Helmuth (University of Bristol) as part of Horowitz seminar on probabil
ity\, ergodic theory and dynamical systems\n\n\nAbstract\nThe arboreal gas
is the probability measure that arises from conditioning the random subgr
aph given by Bernoulli($p$) bond percolation to be a spanning forest\, i.e
.\, to contain no cycles. This conditioning makes sense on any finite grap
h $G$\, and in the case $p=1/2$ gives the uniform measure on spanning fore
sts. The arboreal gas also arises as a $q\\to0$ limit of the $q$-state ran
dom cluster model.\n\nWhat are the percolative properties of these forests
? This turns out to be a surprisingly rich question\, and I will discuss w
hat is known and conjectured. I will also describe a tool for studying con
nection probabilities\, the magic formula\, which arises due to an importa
nt connection between the arboreal gas and spin systems with hyperbolic sy
mmetry.\n\nBased on joint work with Roland Bauerschmidt\, Nick Crawford\,
and Andrew Swan.\n
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:20201029T110621Z
UID:HSPETDS/16
DESCRIPTION:Title: Bounded-displacement non-equivalence in substitution ti
lings\nby Yaar Solomon (Ben-Gurion university of the Negev) as part of Hor
owitz seminar on probability\, ergodic theory and dynamical systems\n\n\nA
bstract\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 bound
ed. This notion induces an equivalence relation on collections $X$ of Delo
ne sets and we study the cardinality of BD($X$)\, a collection of all BD-c
lass representatives. In this talk we focus on sets $X$ of point sets that
correspond to tilings in a substitution tiling space. We provide a suffic
ient condition under which |BD($X$)| is the continuum. In particular we sh
ow that\, in the context of primitive substitution tilings\, |BD($X$)| can
be greater than $1$.\n
END:VEVENT
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