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BEGIN:VEVENT
SUMMARY:Tom Hutchcroft (University of Cambridge)
DTSTART;VALUE=DATE-TIME:20200427T130000Z
DTEND;VALUE=DATE-TIME:20200427T133000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133048Z
UID:LPDD/1
DESCRIPTION:Title: Per
colation on hyperbolic groups\nby Tom Hutchcroft (University of Cambri
dge) as part of Les probabilités de demain webinar\n\n\nAbstract\nMany qu
estions in probability theory concern the way the geometry of a space infl
uences the behaviour of random processes on that space\, and in particular
how the geometry of a space is affected by random perturbations. One of t
he simplest models of such a random perturbation is percolation\, in which
the edges of a graph are either deleted or retained independently at rand
om with retention probability p. We are particularly interested in phase t
ransitions\, in which the geometry of the percolated subgraph undergoes a
qualitative change as p is varied through some special value. Although per
colation has traditionally been studied primarily in the context of Euclid
ean lattices\, the behaviour of percolation in more exotic settings has re
cently attracted a great deal of attention. In this talk\, I will discuss
conjectures and results concerning percolation on the Cayley graphs of non
amenable groups and hyperbolic spaces\, and give a taste of the proof of o
ur recent result that percolation in any hyperbolic graph has a non-trivia
l phase in which there are infinitely many infinite clusters.\n
LOCATION:https://researchseminars.org/talk/LPDD/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Baptiste Cerclé (Université Paris Nord)
DTSTART;VALUE=DATE-TIME:20200427T133000Z
DTEND;VALUE=DATE-TIME:20200427T140000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133048Z
UID:LPDD/2
DESCRIPTION:Title: Lio
uville Conformal Field Theory (in higher dimensions)\nby Baptiste Cerc
lé (Université Paris Nord) as part of Les probabilités de demain webina
r\n\n\nAbstract\nProviding a rigorous definition to the two-dimensional Li
ouville Quantum\nGravity as introduced by Polyakov in his 1981 seminal wor
k has been a\nchallenging problem over the last few years. In this fundame
ntal article\nis introduced a canonical way of picking at random a geometr
y on a\nsurface with fixed topology\, using a generalised path integral ap
proach\ninvolving the Liouville functional. The mathematical interpretatio
n of\nthis formalism is now rather well understood\, thanks to the introdu
ction\nof a probabilistic framework involving two fundamental objects : th
e\nGaussian Multiplicative Chaos and log-correlated fields. During this\nt
alk I will try to introduce this topic\, and if time permits\, present\nso
me recent developments in the higher-dimensional theory.\n
LOCATION:https://researchseminars.org/talk/LPDD/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oriane Blondel (Université Lyon 1)
DTSTART;VALUE=DATE-TIME:20200504T130000Z
DTEND;VALUE=DATE-TIME:20200504T133000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133048Z
UID:LPDD/3
DESCRIPTION:Title: Int
erfaces dans des systèmes de particules avec contraintes cinétique\n
by Oriane Blondel (Université Lyon 1) as part of Les probabilités de dem
ain webinar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/LPDD/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rémy Mahfouf (ENS Paris)
DTSTART;VALUE=DATE-TIME:20200504T133000Z
DTEND;VALUE=DATE-TIME:20200504T140000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133048Z
UID:LPDD/4
DESCRIPTION:Title: Tow
ards universality of Ising model\nby Rémy Mahfouf (ENS Paris) as part
of Les probabilités de demain webinar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/LPDD/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chenlin Gu (ENS Paris)
DTSTART;VALUE=DATE-TIME:20200511T130000Z
DTEND;VALUE=DATE-TIME:20200511T133000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133048Z
UID:LPDD/5
DESCRIPTION:Title: An
efficient algorithm for solving elliptic problems on percolation clusters<
/a>\nby Chenlin Gu (ENS Paris) as part of Les probabilités de demain webi
nar\n\n\nAbstract\nWe present an efficient algorithm to solve elliptic Dir
ichlet problems\ndefined on the cluster of Z^d supercritical Bernoulli per
colation\, as a\ngeneralization of the iterative method proposed by S. Arm
strong\, A.\nHannukainen\, T. Kuusi and J.-C. Mourrat. We also explore the
two-scale\nexpansion on the infinite cluster of percolation\, and use it
to give a\nrigorous analysis of the algorithm.\n
LOCATION:https://researchseminars.org/talk/LPDD/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christina Goldschmidt (University of Oxford)
DTSTART;VALUE=DATE-TIME:20200511T133000Z
DTEND;VALUE=DATE-TIME:20200511T140000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133048Z
UID:LPDD/6
DESCRIPTION:Title: The
scaling limit of a critical random directed graph\nby Christina Golds
chmidt (University of Oxford) as part of Les probabilités de demain webin
ar\n\n\nAbstract\nWe consider the random directed graph $D(n\, p)$ with ve
rtex set $\\{1\, 2\, \\ldots\, n\\}$ in which each of the $n(n − 1)$ pos
sible directed edges is present independently with probability $p$. We are
interested in the strongly connected components of this directed graph. A
phase transition for the emergence of a giant strongly connected componen
t is known to occur at $p = 1/n$\, with critical window $p = 1/n + \\lambd
a n^{-4/3}$ for $\\lambda \\in \\R$. We show that\, within this critical w
indow\, the strongly connected components of $D(n\, p)$\, ranked in decrea
sing order of size and rescaled by $n^{-1/3}$\, converge in distribution t
o a sequence of finite strongly connected directed multigraphs with edge l
engths which are either 3-regular or loops.\n\nThis is joint work with Rob
in Stephenson (University of Sheffield).\n
LOCATION:https://researchseminars.org/talk/LPDD/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antoine Mouzard (Université de Rennes 1)
DTSTART;VALUE=DATE-TIME:20200518T130000Z
DTEND;VALUE=DATE-TIME:20200518T133000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133048Z
UID:LPDD/7
DESCRIPTION:Title: The
continuous Anderson hamiltonian on a two-dimensional manifold\nby Ant
oine Mouzard (Université de Rennes 1) as part of Les probabilités de dem
ain webinar\n\n\nAbstract\nWe construct the continuous Anderson hamiltonia
n driven by a white noise on a compact two-dimensional manifold. We use th
e paracontrolled calculus to define a dense domain that depends on an enha
nced noise built through a renormalisation step\, in the spirit of the rec
ent works on singular SPDEs. Using the Babuška-Lax-Milgram theorem\, it y
ields a self-adjoint operator with pure point spectrum and we have estimat
es for the eigenvalues.\n
LOCATION:https://researchseminars.org/talk/LPDD/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laurent Mazliak (Sorbonne Université)
DTSTART;VALUE=DATE-TIME:20200518T133000Z
DTEND;VALUE=DATE-TIME:20200518T140000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133048Z
UID:LPDD/8
DESCRIPTION:Title: De
Markov à Doeblin : une chaîne avec des sauts\nby Laurent Mazliak (So
rbonne Université) as part of Les probabilités de demain webinar\n\n\nAb
stract\nL'exposé présentera rapidement les deux sources d'intérêt pour
la théorie des « événements en chaîne » au début du 20ème siècle
\, dont la rencontre imprévue a engendré un des principaux courants de r
echerche des probabilités modernes.\n
LOCATION:https://researchseminars.org/talk/LPDD/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxime Berger (ENS Paris)
DTSTART;VALUE=DATE-TIME:20200525T130000Z
DTEND;VALUE=DATE-TIME:20200525T133000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133048Z
UID:LPDD/9
DESCRIPTION:Title: Le
modèle de la quasi-espèce\nby Maxime Berger (ENS Paris) as part of L
es probabilités de demain webinar\n\n\nAbstract\nNous exposerons un modè
le issu de la génétique qui permet de suivre l’évolution d’une popu
lation. Les individus sont soumis aux forces de mutation et de sélection\
, et un équilibre entre ces deux forces est nécessaire pour une évoluti
on optimale. Cet équilibre conduit à une transition de phase dans le mod
èle.\n
LOCATION:https://researchseminars.org/talk/LPDD/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rémi Catellier (Université de Nice Sophia-Antipolis)
DTSTART;VALUE=DATE-TIME:20200525T133000Z
DTEND;VALUE=DATE-TIME:20200525T140000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133048Z
UID:LPDD/10
DESCRIPTION:Title: Co
nvergence for stochastic differential equation: a rough approach\nby R
émi Catellier (Université de Nice Sophia-Antipolis) as part of Les proba
bilités de demain webinar\n\n\nAbstract\nIn this talk\, I briefly present
some sequences of stochastic differential equations\, coming from homogen
ization problems or mean-field problems\, where rough paths techniques are
a real plus to prove the convergence to a limiting object.\n
LOCATION:https://researchseminars.org/talk/LPDD/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Florian Bechtold (Sorbonne Université - UPMC)
DTSTART;VALUE=DATE-TIME:20200615T130000Z
DTEND;VALUE=DATE-TIME:20200615T133000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133048Z
UID:LPDD/11
DESCRIPTION:Title: A
law of large numbers for interacting diffusions via a mild formulation
\nby Florian Bechtold (Sorbonne Université - UPMC) as part of Les probabi
lités de demain webinar\n\n\nAbstract\nConsider a system of n weakly inte
racting particles driven by independent Brownian motions. In many instance
s\, it is well known that the empirical measure converges to the solution
of a partial differential equation\, usually called McKean-Vlasov or Fokke
r-Planck equation\, as n tends to infinity. We propose a relatively new ap
proach to show this convergence by directly studying the stochastic partia
l differential equation that the empirical measure satisfies for each fixe
d n. Under a suitable control on the noise term\, which appears due to the
finiteness of the system\, we are able to prove that the stochastic pertu
rbation goes to zero\, showing that the limiting measure is a solution to
the classical McKean-Vlasov equation. In contrast with known results\, we
do not require any independence or finite moment assumption on the initial
condition\, but the only weak convergence. The evolution of the empirical
measure is studied in a suitable class of Hilbert spaces where the noise
term is controlled using two distinct but complementary techniques: rough
paths theory and maximal inequalities for self-normalized processes.\n
LOCATION:https://researchseminars.org/talk/LPDD/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eveliina Peltola (University of Bonn)
DTSTART;VALUE=DATE-TIME:20200615T133000Z
DTEND;VALUE=DATE-TIME:20200615T140000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133048Z
UID:LPDD/12
DESCRIPTION:Title: Sy
mmetries and Probabilities in Lattice Models\nby Eveliina Peltola (Uni
versity of Bonn) as part of Les probabilités de demain webinar\n\n\nAbstr
act\nIn statistical physics\, one considers random models of large systems
\, whose individual components cannot be studied separately since there ar
e so many of them (e.g.\, in 1g of iron there are approximately 10^22 iron
molecules). Thus\, properties of the system are described in terms of pro
bability theory. Many interesting models\, such as the so-called Ising mod
el (describing magnetic material)\, enjoy symmetries that are useful when
studying features of the model. In particular\, so-called critical lattice
models are symmetric with respect to conformal (injective\, holomorphic)
transformations in a certain sense. In this talk\, we discuss how to make
such a concept mathematically precise and how to understand probabilities
of crossing events in such critical models. These questions have led to in
teresting discoveries in the mathematics community\, such as the celebrate
d Schramm-Loewner evolution random curves and concepts trying to make sens
e of quantum field theory rigorously.\n
LOCATION:https://researchseminars.org/talk/LPDD/12/
END:VEVENT
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