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UID:72@math.technion.ac.il
DTSTART;TZID=Asia/Jerusalem:20230530T113000
DTEND;TZID=Asia/Jerusalem:20230530T123000
DTSTAMP:20230529T065920Z
URL:https://math.technion.ac.il/en/events/gady-kozma-weizmann/
SUMMARY:The correlation length of near-critical percolation
DESCRIPTION:Lecturer:Gady Kozma (Weizmann)\n Location:Meyer building (elect
rical engeneering)\, room 861\n Since the works of Menshikov and Aizenman-
Barsky it is known that for every p below the critical value for percolati
on\, the probability that two distant points are connected decays exponent
ially. The constant in the exponent is called the correlation length. We e
stablish bounds for the correlation length as p increases to the critical
value valid in any dimension. Joint work with Hugo Duminil-Copin and Vince
nt Tassion.\n
CATEGORIES:Probability Seminar
END:VEVENT
BEGIN:VEVENT
UID:87@math.technion.ac.il
DTSTART;TZID=Asia/Jerusalem:20230606T113000
DTEND;TZID=Asia/Jerusalem:20230606T123000
DTSTAMP:20230605T093221Z
URL:https://math.technion.ac.il/en/events/tightness-for-the-cover-time-of-
wired-planar-domains/
SUMMARY:Tightness for the Cover Time of Wired Planar Domains
DESCRIPTION:Lecturer:Oren Louidor (Technion)\n Location:Meyer (EE) 861\n We
consider a continuous time simple random walk on a subset of the square l
attice with wired boundary conditions: The walk transitions at unit edge r
ate on the graph obtained from the lattice closure of the subset by contra
cting the boundary into one vertex. We study the cover time of such walk\,
namely the time it takes for the walk to visit all vertices in the graph.
Taking a sequence of subsets obtained as scaled lattice versions of a nic
e planar domain\, we show that the square root of the cover time normalize
d by the size of the subset\, is tight around \\frac{1}{\\sqrt{\\pi}} \\lo
g N - \\frac{1}{4 \\sqrt{\\pi}} \\log \\log N\, where N is the scale param
eter. The proof is based on comparison with the extremal landscape of the
discrete Gaussian free field. Joint work with Marek Biskup and Santiago Sa
glietti.\n
CATEGORIES:Probability Seminar
END:VEVENT
BEGIN:VEVENT
UID:95@math.technion.ac.il
DTSTART;TZID=Asia/Jerusalem:20230613T113000
DTEND;TZID=Asia/Jerusalem:20230613T123000
DTSTAMP:20230619T062715Z
URL:https://math.technion.ac.il/en/events/tba-jonathan-hermon-ubc/
SUMMARY:Quantitative near-bipartiteness: mixing\, parity breaking\, max cut
\, and eigenvalue gap
DESCRIPTION:Lecturer:Jonathan Hermon (UBC)\n Location:Meyer building (elect
rical engeneering)\, room 861\n In this talk I'll present some general qua
ntitative near-bipartite results for reversible Markov chains. It turns ou
t that if the total variation of a reversible transition matrix P is much
larger than that of its lazy version (I+P)/2 then P must satisfy certain s
trong near-bipartite behaviors\, which for most starting states prevail fo
r order of the mixing time number of steps. Namely\, if f is an eigenvecto
r corresponding to the smallest eigenvalue of P\, then the chain is likely
to alternate between being at A:={x : f(x) is positive} at even times to
being at the complement at odd times\, or vice-versa\, for order mixing ti
me number of steps. Moreover\, the mixing behavior in this case is in a se
nse completely governed by the probability the chain assigns A. We also g
ive a probabilistic characterization of the absolute spectral gap of P and
show that P can have at most one (negative) eigenvalue whose distance fro
m -1 is at most a small absolute constant the spectral gap (= 1 - second l
argest e.v. of P)\n
CATEGORIES:Probability Seminar
END:VEVENT
BEGIN:VEVENT
UID:105@math.technion.ac.il
DTSTART;TZID=Asia/Jerusalem:20230620T113000
DTEND;TZID=Asia/Jerusalem:20230620T123000
DTSTAMP:20230619T062541Z
URL:https://math.technion.ac.il/en/events/generalized-chase-escape-models-
and-weighted-catalan-numbers/
SUMMARY:Generalized chase-escape models and weighted Catalan numbers
DESCRIPTION:Lecturer:Saraí Hernández-Torres (Instituto de Matemáticas\,
UNAM)\n Location:Meyer building (electrical engeneering)\, room 861\n In t
his talk\, Wwe will present a relation between weighted Catalan numbers an
d the phase transitions of a competitive growth process on a d-ary tree. T
he competitive growth processes presenting this relation are generalizatio
ns of chase-escape: chase-escape with death and distance-dependent chase-e
scape\, which mimic the dynamics of a predator chasing prey\, and the latt
er have random lifespans.This talk is based on joint works with Erin Beckm
an\, Keisha Cook\, Nicole Eikmeier\, and Matthew Junge\; and with Matthew
Junge\, Naina Ray and Nidhi Ray.\n
CATEGORIES:Probability Seminar
END:VEVENT
BEGIN:VEVENT
UID:109@math.technion.ac.il
DTSTART;TZID=Asia/Jerusalem:20230704T113000
DTEND;TZID=Asia/Jerusalem:20230704T123000
DTSTAMP:20230702T204200Z
URL:https://math.technion.ac.il/en/events/extrema-of-two-dimensional-ginzb
urg-landau-fields/
SUMMARY:Extrema of two-dimensional Ginzburg-Landau fields
DESCRIPTION:Lecturer: Florian Schweiger (Weizmann)\n Location:Meyer (EE) 86
1\n Ginzburg-Landau fields (also known as $\nabla\\phi$-models) are a clas
s of a models from statistical mechanics that describe the behavior of int
erfaces. In the talk I will introduce these models and survey some of the
known results. I will then describe ongoing joint work with Wei Wu and Ofe
r Zeitouni on the asymptotics of the maximum of these models in two dimens
ions.\n
CATEGORIES:Probability Seminar
END:VEVENT
BEGIN:VEVENT
UID:147@math.technion.ac.il
DTSTART;TZID=Asia/Jerusalem:20240109T113000
DTEND;TZID=Asia/Jerusalem:20240109T123000
DTSTAMP:20240107T135125Z
URL:https://math.technion.ac.il/en/events/double-bubble-problem-in-non-iso
tropic-norms/
SUMMARY:Double bubble problem in non-isotropic norms
DESCRIPTION:Lecturer:Parker Duncan (Technion)\n Location:Meyer (EE) 861\n T
he Double Bubble problem asks the following: given two volumes\, what are
the two shapes admitting these volumes with the smallest perimeter\, where
the perimeter of the joint boundary is counted once. While past solutions
focused on rotationally invariant norms\, our work addresses non-isotropi
c scenarios found in crystalline structures and lattice-based soup bubbles
. We present three results: the first provides a solution to the Double Bu
bble problem in the taxicab metric using elementary principles\, the secon
d shows that the solution to the discrete double bubble problem in the tax
icab metric is at most two more than the ceiling function of the continuou
s solution\, and the final result presents the solution to the Double Bubb
le problem in the hexagonal norm. The works consist of new geometric and
discrete optimization techniques.\nJoint work with Eviatar Procaccia and
Rory O’Dwyer\n
CATEGORIES:Probability Seminar
END:VEVENT
BEGIN:VEVENT
UID:162@math.technion.ac.il
DTSTART;TZID=Asia/Jerusalem:20240130T113000
DTEND;TZID=Asia/Jerusalem:20240130T123000
DTSTAMP:20240129T212506Z
URL:https://math.technion.ac.il/en/events/eviatar-procaccia-technion-verte
x-removal-stability-and-the-least-positive-value-of-harmonic-measures/
SUMMARY:Eviatar Procaccia (Technion) -- Vertex-removal stability and the le
ast positive value of harmonic measures
DESCRIPTION:Lecturer:Eviatar Procaccia (Technion)\n Location:Meyer (EE) 861
\n We prove that for Z^d (d>\;1)\, the vertex-removal stability of harmo
nic measures (i.e. it is feasible to remove some vertex while changing the
harmonic measure by a bounded factor) holds if and only if d=2. The proof
mainly relies on geometric arguments\, with a surprising use of the discr
ete Klein bottle. Moreover\, a direct application of this stability verifi
es a conjecture of Calvert\, Ganguly and Hammond\, for the exponential dec
ay of the least positive value of harmonic measures on Z^2. Furthermore\,
the analogue of this conjecture for Z^d with d>\; 2 is also proved in th
is paper\, despite vertex-removal stability no longer holding.\n
CATEGORIES:Probability Seminar
END:VEVENT
BEGIN:VEVENT
UID:167@math.technion.ac.il
DTSTART;TZID=Asia/Jerusalem:20240206T113000
DTEND;TZID=Asia/Jerusalem:20240206T123000
DTSTAMP:20240205T083617Z
URL:https://math.technion.ac.il/en/events/noise-sensitivity-governed-by-ra
ndom-walks-on-the-symmetric-group/
SUMMARY:Noise Sensitivity Governed by Random Walks on the Symmetric Group
DESCRIPTION:Lecturer:Subhajit Ghosh\n Location:Meyer building (electrical e
ngeneering)\, room 861\n In this talk\, we focus on the Boolean functions
on the\nsymmetric group. The noise sources are various continuous-time ran
dom\nwalks on the symmetric group. First\, we focus on the continuous-time
\nrandom transposition walk\, and state equivalent criterion for noise\nse
nsitivity and noise stability. These involve the Fourier\ntransformation o
f the given function at irreducible representations (of\nthe symmetric gro
up). We use them to study the sensitivity/stability\nnature of some Boolea
n functions\, viz.\, the parity function\, the\ndictator function\, and th
e indicator of the set of permutations with\n``long" cycles. Finally\, we
give some comparison results when the noise\nsource is other continuous-ti
me random walks\, viz. the star\ntransposition\, $s$-cycles ($s$ is even a
nd ``small enough"). The\ntechniques used in this talk are based on the re
presentation theory of\nthe symmetric group.\nThis is based on an ongoing
work in progress with Gideon Amir.\n
CATEGORIES:Probability Seminar
END:VEVENT
BEGIN:VEVENT
UID:184@math.technion.ac.il
DTSTART;TZID=Asia/Jerusalem:20240213T113000
DTEND;TZID=Asia/Jerusalem:20240213T123000
DTSTAMP:20240212T073040Z
URL:https://math.technion.ac.il/en/events/a-sharp-transition-in-the-zero-c
ount-of-stationary-gaussian-processes/
SUMMARY:A sharp transition in the zero count of stationary Gaussian process
es
DESCRIPTION:Lecturer:Lakshmi Priya (TAU)\n Location:Meyer building (electri
cal engeneering)\, room 861\n We study an aspect of the zeros of centered
stationary Gaussianprocesses (SGP) on R\, namely NT\, which is the number
of zeros in theinterval [0\,T]. In earlier studies\, under varying assumpt
ions on thespectral measure of the SGP\, the following results/statistics
wereobtained for NT: expectation\, variance asymptotics\, CLT\, exponentia
lconcentration\, overcrowding estimates\, and finiteness of moments.We wil
l restrict our attention to SGP with compactly supported spectralmeasure
μ. Let A >\; 0 be the smallest number such that supp(μ) ⊆ [−A\, A]
.Stationarity of the process implies that the expectation of NT ispropor
tional to T. Our primary interest is in overcrowding (resp. undercrowding)
probability\, which is the probability of the event that thereis an exces
s (resp. deficit) of zeros in [0\,T] compared to the expectednumber. Compa
ring a couple of known results\, we can conclude that thereis a change in
the behaviour of the probability P(NT ≥ ηT)\, as η varies.We show that
there is indeed a sharp transition. That is\, thisprobability is at least
of the order of exp(−CηT) for small η\, and atmost of order exp(−c
ηT2) for large η. We will also identify the criticalη where this transi
tion happens to be ηc = A/π. We also prove a similarresult for under cro
wding probability when supp(μ) has a gap at the origin.This talk is based
on a joint work with Naomi Feldheim &\; Ohad Feldheim.\n
CATEGORIES:Probability Seminar
END:VEVENT
BEGIN:VEVENT
UID:187@math.technion.ac.il
DTSTART;TZID=Asia/Jerusalem:20240220T113000
DTEND;TZID=Asia/Jerusalem:20240220T123000
DTSTAMP:20240213T124031Z
URL:https://math.technion.ac.il/en/events/large-deviations-theory-for-chem
ical-reaction-networks/
SUMMARY:Large deviations theory for chemical reaction networks.
DESCRIPTION:Lecturer:Amir Dembo (Stanford) \n Location:Meyer building (elec
trical engeneering)\, room 861\n Title: Scaling limits for growth driven b
y reflecting Brownian motion\n \;\nAbstract: In joint works with Kevin
Yang\, we consider a stochastic Laplacian growth model\, that can be view
ed as a continuum version of origin-excited random walks. Here\, we grow t
he (d+1)-dimensional manifold M(t) according to a reflecting Brownian moti
on (RBM) on M(t)\, stopped at level sets of its boundary local time. An av
eraging principle for the RBM characterizes the scaling limit for the lead
ing order behavior of the interface (namely\, the boundary of M(t)). This
limit is given by a locally well-posed\, geometric flow-type PDE\, whose b
low-up times correspond to changes in the diffeomorphism class of the grow
ing set. Smoothing the interface as we inflate M(t)\, yields an SPDE for t
he large-scale fluctuations of an associated height function. This SPDE is
a regularized KPZ-type equation\, modulated by a Dirichlet-to-Neumann ope
rator. For d=1 we can further remove the regularization\, so the fluctuati
ons of M(t) now have a double-scaling limit given by a singular KPZ-type e
quation.\n
CATEGORIES:Probability Seminar
END:VEVENT
BEGIN:VEVENT
UID:221@math.technion.ac.il
DTSTART;TZID=Asia/Jerusalem:20240402T103000
DTEND;TZID=Asia/Jerusalem:20240402T113000
DTSTAMP:20240416T055920Z
URL:https://math.technion.ac.il/en/events/stochastic-differential-equation
s-involving-the-local-time-of-the-unknown-process-driven-by-stable/
SUMMARY:Stochastic Differential Equations Involving the Local Time of the U
nknown Process Driven by Stable
DESCRIPTION:Lecturer:Johanna Weinberger (Technion)\n Location:Meyer buildin
g (electrical engeneering)\, room 861\n We consider singular SDEs driven b
y symmetric stable processes and with measure valued drift in a Kato class
. Since the drift may be a measure which is not absolutely continuous one
needs to find a rigorous definition of solutions. This can\, for instance\
, be achieved by employing an approximation scheme [Kim &\; Song\, '14]
. We show that we can equivalently reformulate the drift term in terms of
the local time of the unknown process. To this end\, we derive a Tanaka-
type formula for symmetric stable processes that are perturbed by an adapt
ed\, right-continuous processes of finite variation. Finally\, we discuss
weak and strong existence and uniqueness of solutions.\n
CATEGORIES:Probability Seminar
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