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BEGIN:VEVENT
SUMMARY:Persi Diaconis (Stanford University)
DTSTART;VALUE=DATE-TIME:20201013T130000Z
DTEND;VALUE=DATE-TIME:20201013T140000Z
DTSTAMP;VALUE=DATE-TIME:20230925T222013Z
UID:PSA/1
DESCRIPTION:Title: The
Mathematics of making a mess (an introduction to random walk on groups)\nby Persi Diaconis (Stanford University) as part of Probability and Stoc
hastic Analysis at Tecnico Lisboa\n\n\nAbstract\nHow many random transposi
tions does it take to mix up $n$ cards? This is a typical question of rand
om walk on finite groups. The answer is $\\frac{1}{2}n \\log{n} + Cn$ and
there is a sharp phase transition from order to chaos as $C$ varies. The t
echniques involve Fourier analysis on non-commutative groups (which I will
try to explain for non specialists). As you change the group or change th
e walk\, new analytic and algebraic tools are required. The subject has wi
de applications (people still shuffle cards\, but there are applications i
n physics\, chemistry\,biology and computer science — even for random tr
anspositions). Extending to compact or more general groups opens up many p
roblems. This was the first problem where the ‘cutoff phenomenon’ was
observed and this has become a healthy research area.\n
LOCATION:https://researchseminars.org/talk/PSA/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nina Gantert (Technische Universität München)
DTSTART;VALUE=DATE-TIME:20201110T140000Z
DTEND;VALUE=DATE-TIME:20201110T150000Z
DTSTAMP;VALUE=DATE-TIME:20230925T222013Z
UID:PSA/2
DESCRIPTION:Title: Mixi
ng times for the simple exclusion process with open boundaries\nby Nin
a Gantert (Technische Universität München) as part of Probability and St
ochastic Analysis at Tecnico Lisboa\n\n\nAbstract\nWe study mixing times o
f the symmetric and asymmetric simple exclusion process on the segment whe
re particles are allowed to enter and exit at the endpoints. We consider d
ifferent regimes depending on the entering and exiting rates as well as on
the rates in the bulk\, and show that the process exhibits pre-cutoff and
in some special cases even cutoff.\n
LOCATION:https://researchseminars.org/talk/PSA/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claudio Landim (Instituto Nacional de Matemática Pura e Aplicada
(IMPA))
DTSTART;VALUE=DATE-TIME:20201215T140000Z
DTEND;VALUE=DATE-TIME:20201215T150000Z
DTSTAMP;VALUE=DATE-TIME:20230925T222013Z
UID:PSA/3
DESCRIPTION:Title: Stat
ic large deviations for a reaction-diffusion model\nby Claudio Landim
(Instituto Nacional de Matemática Pura e Aplicada (IMPA)) as part of Prob
ability and Stochastic Analysis at Tecnico Lisboa\n\n\nAbstract\nWe examin
e the stationary state of an interacting particle system whose macroscopic
evolution is described by one-dimensional reaction-diffusion equations.\n
LOCATION:https://researchseminars.org/talk/PSA/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Serguei Popov (Universidade de Porto)
DTSTART;VALUE=DATE-TIME:20210112T140000Z
DTEND;VALUE=DATE-TIME:20210112T150000Z
DTSTAMP;VALUE=DATE-TIME:20230925T222013Z
UID:PSA/4
DESCRIPTION:Title: Cond
itioned SRW in two dimensions and some of its surprising properties\nb
y Serguei Popov (Universidade de Porto) as part of Probability and Stochas
tic Analysis at Tecnico Lisboa\n\n\nAbstract\nWe consider the two-dimensio
nal simple random walk conditioned on never hitting the origin. This proce
ss is a Markov chain\, namely it is the Doob $h$-transform of the simple r
andom walk\nwith respect to the potential kernel. It is known to be transi
ent and we show that it is "almost recurrent" in the sense that each infin
ite set is visited infinitely often\, almost surely. After discussing some
basic properties of this process (in particular\, calculating its Green's
function)\, we prove that\, for a "large" set\, the proportion of its sit
es visited by the conditioned walk is approximately a Uniform$[0\,1]$ rand
om variable. Also\, given a set $G\\subset R^2$ that does not "surround" t
he origin\, we prove that a.s. there is an infinite number of $k$'s such t
hat $kG\\cap Z^2$ is unvisited. These results suggest that the range of th
e conditioned walk has "fractal" behavior. Also\, we obtain estimates on t
he speed of escape of the walk to infinity\, and prove that\, in spite of
transience\, two independent copies of conditioned walks will a.s. meet in
finitely many tim\n
LOCATION:https://researchseminars.org/talk/PSA/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre Tarrès (New York University Shanghai)
DTSTART;VALUE=DATE-TIME:20210209T140000Z
DTEND;VALUE=DATE-TIME:20210209T150000Z
DTSTAMP;VALUE=DATE-TIME:20230925T222013Z
UID:PSA/5
DESCRIPTION:Title: Rein
forced random walks and statistical physics\nby Pierre Tarrès (New Yo
rk University Shanghai) as part of Probability and Stochastic Analysis at
Tecnico Lisboa\n\n\nAbstract\nWe explain how the Edge-reinforced random wa
lk\, introduced by \nCoppersmith and Diaconis in 1986\, is related to seve
ral models in \nstatistical physics\, namely the supersymmetric hyperbolic
sigma model \nstudied by Disertori\, Spencer and Zirnbauer (2010)\, the r
andom \nSchrödinger operator and Dynkin's isomorphism.\n\nWe also discuss
recent non-reversible generalizations of the ERRW and the VRJP. Based on
joint works (or work in progress) with C. Sabot\, X. Zeng\, T. Lupu\, M. D
isertori and S. Baccalado.\n
LOCATION:https://researchseminars.org/talk/PSA/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cristian Giardinà (Università degli Studi di Modena e Reggio Emi
lia)
DTSTART;VALUE=DATE-TIME:20210317T170000Z
DTEND;VALUE=DATE-TIME:20210317T180000Z
DTSTAMP;VALUE=DATE-TIME:20230925T222013Z
UID:PSA/6
DESCRIPTION:Title: Exac
t solution of an integrable particle system\nby Cristian Giardinà (Un
iversità degli Studi di Modena e Reggio Emilia) as part of Probability an
d Stochastic Analysis at Tecnico Lisboa\n\n\nAbstract\nWe consider the fam
ily of boundary-driven models introduced in [FGK] and show they can be sol
ved exactly\, i.e. the correlations functions and the non-equilibrium stea
dy-state have a closed-form expression. \n\nThe solution relies on probabi
listic arguments and techniques inspired by integrable systems. As in the
context of bulk-driven systems (scaling to KPZ)\, it is obtained in two st
eps: i) the introduction of a dual process\; ii) the solution of the dual
dynamics by Bethe ansatz. \n\nFor boundary-driven systems\, a general by
-product of duality is the existence of a direct mapping (a conjugation) b
etween the generator of the non-equilibrium process and the generator of t
he associated reversible equilibrium process. Macroscopically\, this mappi
ng was observed years ago by Tailleur\, Kurchan and Lecomte in the context
of the Macroscopic Fluctuation Theory.\n\n[FGK] R. Frassek\, C. Giardinà
\, J. Kurchan\, Non-compact quantum spin chains as integrable stochastic p
article processes\, Journal of Statistical Physics 180\, 366-397 (2020).\n
\nZoom password: 958 0581 3232\n
LOCATION:https://researchseminars.org/talk/PSA/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yinon Spinka (University of British Columbia)
DTSTART;VALUE=DATE-TIME:20210421T160000Z
DTEND;VALUE=DATE-TIME:20210421T170000Z
DTSTAMP;VALUE=DATE-TIME:20230925T222013Z
UID:PSA/7
DESCRIPTION:Title: A ta
le of two balloons\nby Yinon Spinka (University of British Columbia) a
s part of Probability and Stochastic Analysis at Tecnico Lisboa\n\n\nAbstr
act\nFrom each point of a Poisson point process start growing a balloon at
rate 1. When two balloons touch\, they pop and disappear. Will balloons r
each the origin infinitely often or not? We answer this question for vario
us underlying spaces. En route we find a new(ish) 0-1 law\, and generalize
bounds on independent sets that are factors of IID on trees. Joint work w
ith Omer Angel and Gourab Ray.\n
LOCATION:https://researchseminars.org/talk/PSA/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tal Orenshtein (WIAS\, TU-Berlin)
DTSTART;VALUE=DATE-TIME:20210519T160000Z
DTEND;VALUE=DATE-TIME:20210519T170000Z
DTSTAMP;VALUE=DATE-TIME:20230925T222013Z
UID:PSA/8
DESCRIPTION:Title: Roug
h walks in random environment\nby Tal Orenshtein (WIAS\, TU-Berlin) as
part of Probability and Stochastic Analysis at Tecnico Lisboa\n\n\nAbstra
ct\nRandom walks in random environment (RWRE) have been extensively studie
d in the last half-century. Functional central limit theorems (FCLT) hold
in some prototypical classes such the reversible and the ballistic ones. T
he latter are treated using rather different techniques\; Kipnis-Varadhan'
s theory for additive functionals of Markov processes is applicable in the
reversible case whereas the main feature exploited in the ballistic class
is a regeneration structure. Rough path theory is a deterministic theory
which extends classical notions of integration to singular integrators in
a continuous manner. It typically provides a framework for pathwise soluti
ons of ordinary and partial stochastic differential equations driven by a
singular noise. In the talk we shall discuss FCLT for additive functionals
of Markov processes and regenerative processes lifted to the rough path s
pace. The limiting rough path has two levels. The first one is the Brownia
n motion\, whereas in the second we see a new feature: it is the iterated
integral of the Brownian motion perturbed by a deterministic linear functi
on called the area anomaly. The aforementioned classes of RWRE are covered
as special cases. The results provide sharper information on the limiting
path. In addition\, the construction of new examples for SDE approximatio
ns is an immediate application.\n\nBased on collaborations (some still in
progress) with Johannes Bäumler\, Noam Berger\, Jean-Dominique Deuschel\,
Olga Lopusanschi\, Nicolas Perkowski and Martin Slowik.\n\nReferences:\n\
n1) Additive functionals as rough paths\, with Jean-Dominique Deuschel and
Nicolas Perkowski\, Ann. Probab. 49(3): 1450-1479 (May 2021). DOI: 10.121
4/20-AOP1488.\n\n2) Ballistic random walks in random environment as rough
paths: convergence and area anomaly\, with Olga Lopusanschi\, ALEA\, Lat.
Am. J. Probab. Math. Stat. 18\, 945–962 (April 2021) DOI: 10.30757/ALEA
.v18-34.\n\n3) Rough invariance principle for delayed regenerative process
es\, arXiv:2101.05222.\n
LOCATION:https://researchseminars.org/talk/PSA/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugene Speer (Rutgers University)
DTSTART;VALUE=DATE-TIME:20210526T160000Z
DTEND;VALUE=DATE-TIME:20210526T170000Z
DTSTAMP;VALUE=DATE-TIME:20230925T222013Z
UID:PSA/9
DESCRIPTION:Title: Faci
litated Exclusion Processes\nby Eugene Speer (Rutgers University) as p
art of Probability and Stochastic Analysis at Tecnico Lisboa\n\n\nAbstract
\nFacilitated exclusion processes are lattice gasses in which a particle w
ith an empty neighboring site can jump to that site only if it has also an
occupied neighboring site. We will discuss three such models in one dimen
sion\, for both discrete-time and continuous-time dynamics and with varyin
g degrees of asymmetry. We address two questions: What are the possible tr
anslation invariant stationary states? If the initial state is Bernoulli\,
what is the final state? This is joint work with Arvind Ayyer\, Shelly Go
ldstein\, and Joel Lebowitz.\n
LOCATION:https://researchseminars.org/talk/PSA/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marianna Russkikh (Massachusetts Institute of Technology)
DTSTART;VALUE=DATE-TIME:20210616T160000Z
DTEND;VALUE=DATE-TIME:20210616T170000Z
DTSTAMP;VALUE=DATE-TIME:20230925T222013Z
UID:PSA/10
DESCRIPTION:Title: Loz
enge tilings and the Gaussian free field on a cylinder\nby Marianna Ru
sskikh (Massachusetts Institute of Technology) as part of Probability and
Stochastic Analysis at Tecnico Lisboa\n\n\nAbstract\nWe discuss new result
s on lozenge tilings on an infinite cylinder\, which may be analyzed using
the periodic Schur process introduced by Borodin. Under one variant of th
e $q^{vol}$ measure\, corresponding to random cylindric partitions\, the h
eight function converges to a deterministic limit shape and fluctuations a
round it are given by the Gaussian free field in the conformal structure p
redicted by the Kenyon-Okounkov conjecture. Under another variant\, corres
ponding to an unrestricted tiling model on the cylinder\, the fluctuations
are given by the same Gaussian free field with an additional discrete Gau
ssian shift component. Fluctuations of the latter type have been previousl
y conjectured by Gorin for tiling models on planar domains with holes. Thi
s talk is based on joint work with Andrew Ahn and Roger Van Peski.\n
LOCATION:https://researchseminars.org/talk/PSA/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Servet Martínez (Universidad de Chile)
DTSTART;VALUE=DATE-TIME:20210630T160000Z
DTEND;VALUE=DATE-TIME:20210630T170000Z
DTSTAMP;VALUE=DATE-TIME:20230925T222013Z
UID:PSA/11
DESCRIPTION:Title: Dis
crete-time evolution in recombination\nby Servet Martínez (Universida
d de Chile) as part of Probability and Stochastic Analysis at Tecnico Lisb
oa\n\n\nAbstract\nWe study the discrete-time evolution of a recombination
transformation in population genetics acting on the set of measures on gen
etic sequences. The evolution can be described by a Markov chain on the se
t of partitions that converges to the finest partition. We describe the ge
ometric decay rate to the limit and the quasi-stationary behavior when con
ditioned that the chain has not hit the limit.\n
LOCATION:https://researchseminars.org/talk/PSA/11/
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