BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Tom Hutchcroft (University of Cambridge) DTSTART:20200427T130000Z DTEND:20200427T133000Z DTSTAMP:20260404T110829Z UID:LPDD/1 DESCRIPTION:Title: Percolation on hyperbolic groups\nby Tom Hutchcroft (University of Cambridge) as part of Les probabilités de demain webinar\n\n\nAbstract\n Many questions in probability theory concern the way the geometry of a spa ce influences the behaviour of random processes on that space\, and in par ticular how the geometry of a space is affected by random perturbations. O ne of the simplest models of such a random perturbation is percolation\, i n which the edges of a graph are either deleted or retained independently at random with retention probability p. We are particularly interested in phase transitions\, in which the geometry of the percolated subgraph under goes a qualitative change as p is varied through some special value. Altho ugh percolation has traditionally been studied primarily in the context of Euclidean lattices\, the behaviour of percolation in more exotic settings has recently attracted a great deal of attention. In this talk\, I will d iscuss conjectures and results concerning percolation on the Cayley graphs of nonamenable groups and hyperbolic spaces\, and give a taste of the pro of of our recent result that percolation in any hyperbolic graph has a non -trivial phase in which there are infinitely many infinite clusters.\n LOCATION:https://stable.researchseminars.org/talk/LPDD/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Baptiste Cerclé (Université Paris Nord) DTSTART:20200427T133000Z DTEND:20200427T140000Z DTSTAMP:20260404T110829Z UID:LPDD/2 DESCRIPTION:Title: Liouville Conformal Field Theory (in higher dimensions)\nby Baptis te Cerclé (Université Paris Nord) as part of Les probabilités de demain webinar\n\n\nAbstract\nProviding a rigorous definition to the two-dimensi onal Liouville Quantum\nGravity as introduced by Polyakov in his 1981 semi nal work has been a\nchallenging problem over the last few years. In this fundamental article\nis introduced a canonical way of picking at random a geometry on a\nsurface with fixed topology\, using a generalised path inte gral approach\ninvolving the Liouville functional. The mathematical interp retation of\nthis formalism is now rather well understood\, thanks to the introduction\nof a probabilistic framework involving two fundamental objec ts : the\nGaussian Multiplicative Chaos and log-correlated fields. During this\ntalk I will try to introduce this topic\, and if time permits\, pres ent\nsome recent developments in the higher-dimensional theory.\n LOCATION:https://stable.researchseminars.org/talk/LPDD/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Oriane Blondel (Université Lyon 1) DTSTART:20200504T130000Z DTEND:20200504T133000Z DTSTAMP:20260404T110829Z UID:LPDD/3 DESCRIPTION:Title: Interfaces dans des systèmes de particules avec contraintes cinétiqu e\nby Oriane Blondel (Université Lyon 1) as part of Les probabilités de demain webinar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/LPDD/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Rémy Mahfouf (ENS Paris) DTSTART:20200504T133000Z DTEND:20200504T140000Z DTSTAMP:20260404T110829Z UID:LPDD/4 DESCRIPTION:Title: Towards universality of Ising model\nby Rémy Mahfouf (ENS Paris) as part of Les probabilités de demain webinar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/LPDD/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Chenlin Gu (ENS Paris) DTSTART:20200511T130000Z DTEND:20200511T133000Z DTSTAMP:20260404T110829Z UID:LPDD/5 DESCRIPTION:Title: An efficient algorithm for solving elliptic problems on percolation cl usters\nby Chenlin Gu (ENS Paris) as part of Les probabilités de dema in webinar\n\n\nAbstract\nWe present an efficient algorithm to solve ellip tic Dirichlet problems\ndefined on the cluster of Z^d supercritical Bernou lli percolation\, as a\ngeneralization of the iterative method proposed by S. Armstrong\, A.\nHannukainen\, T. Kuusi and J.-C. Mourrat. We also expl ore the two-scale\nexpansion on the infinite cluster of percolation\, and use it to give a\nrigorous analysis of the algorithm.\n LOCATION:https://stable.researchseminars.org/talk/LPDD/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Christina Goldschmidt (University of Oxford) DTSTART:20200511T133000Z DTEND:20200511T140000Z DTSTAMP:20260404T110829Z UID:LPDD/6 DESCRIPTION:Title: The scaling limit of a critical random directed graph\nby Christin a Goldschmidt (University of Oxford) as part of Les probabilités de demai n webinar\n\n\nAbstract\nWe consider the random directed graph $D(n\, p)$ with vertex set $\\{1\, 2\, \\ldots\, n\\}$ in which each of the $n(n − 1)$ possible directed edges is present independently with probability $p$. We are interested in the strongly connected components of this directed g raph. A phase transition for the emergence of a giant strongly connected c omponent is known to occur at $p = 1/n$\, with critical window $p = 1/n + \\lambda n^{-4/3}$ for $\\lambda \\in \\R$. We show that\, within this cri tical window\, the strongly connected components of $D(n\, p)$\, ranked in decreasing order of size and rescaled by $n^{-1/3}$\, converge in distrib ution to a sequence of finite strongly connected directed multigraphs with edge lengths which are either 3-regular or loops.\n\nThis is joint work w ith Robin Stephenson (University of Sheffield).\n LOCATION:https://stable.researchseminars.org/talk/LPDD/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Antoine Mouzard (Université de Rennes 1) DTSTART:20200518T130000Z DTEND:20200518T133000Z DTSTAMP:20260404T110829Z UID:LPDD/7 DESCRIPTION:Title: The continuous Anderson hamiltonian on a two-dimensional manifold\ nby Antoine Mouzard (Université de Rennes 1) as part of Les probabilités de demain webinar\n\n\nAbstract\nWe construct the continuous Anderson ham iltonian driven by a white noise on a compact two-dimensional manifold. We use the paracontrolled calculus to define a dense domain that depends on an enhanced noise built through a renormalisation step\, in the spirit of the recent works on singular SPDEs. Using the Babuška-Lax-Milgram theorem \, it yields a self-adjoint operator with pure point spectrum and we have estimates for the eigenvalues.\n LOCATION:https://stable.researchseminars.org/talk/LPDD/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Laurent Mazliak (Sorbonne Université) DTSTART:20200518T133000Z DTEND:20200518T140000Z DTSTAMP:20260404T110829Z UID:LPDD/8 DESCRIPTION:Title: De Markov à Doeblin : une chaîne avec des sauts\nby Laurent Mazl iak (Sorbonne Université) as part of Les probabilités de demain webinar\ n\n\nAbstract\nL'exposé présentera rapidement les deux sources d'intér êt pour la théorie des « événements en chaîne » au début du 20ème siècle\, dont la rencontre imprévue a engendré un des principaux coura nts de recherche des probabilités modernes.\n LOCATION:https://stable.researchseminars.org/talk/LPDD/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Maxime Berger (ENS Paris) DTSTART:20200525T130000Z DTEND:20200525T133000Z DTSTAMP:20260404T110829Z UID:LPDD/9 DESCRIPTION:Title: Le modèle de la quasi-espèce\nby Maxime Berger (ENS Paris) as pa rt of Les probabilités de demain webinar\n\n\nAbstract\nNous exposerons u n modèle issu de la génétique qui permet de suivre l’évolution d’u ne population. Les individus sont soumis aux forces de mutation et de sél ection\, et un équilibre entre ces deux forces est nécessaire pour une évolution optimale. Cet équilibre conduit à une transition de phase dan s le modèle.\n LOCATION:https://stable.researchseminars.org/talk/LPDD/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Rémi Catellier (Université de Nice Sophia-Antipolis) DTSTART:20200525T133000Z DTEND:20200525T140000Z DTSTAMP:20260404T110829Z UID:LPDD/10 DESCRIPTION:Title: Convergence for stochastic differential equation: a rough approach\nby Rémi Catellier (Université de Nice Sophia-Antipolis) as part of Le s probabilités de demain webinar\n\n\nAbstract\nIn this talk\, I briefly present some sequences of stochastic differential equations\, coming from homogenization problems or mean-field problems\, where rough paths techniq ues are a real plus to prove the convergence to a limiting object.\n LOCATION:https://stable.researchseminars.org/talk/LPDD/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Florian Bechtold (Sorbonne Université - UPMC) DTSTART:20200615T130000Z DTEND:20200615T133000Z DTSTAMP:20260404T110829Z UID:LPDD/11 DESCRIPTION:Title: A law of large numbers for interacting diffusions via a mild formulat ion\nby Florian Bechtold (Sorbonne Université - UPMC) as part of Les probabilités de demain webinar\n\n\nAbstract\nConsider a system of n weak ly interacting particles driven by independent Brownian motions. In many i nstances\, it is well known that the empirical measure converges to the so lution of a partial differential equation\, usually called McKean-Vlasov o r Fokker-Planck equation\, as n tends to infinity. We propose a relatively new approach to show this convergence by directly studying the stochastic partial differential equation that the empirical measure satisfies for ea ch fixed 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 stochasti c perturbation goes to zero\, showing that the limiting measure is a solut ion to the classical McKean-Vlasov equation. In contrast with known result s\, we do not require any independence or finite moment assumption on the initial condition\, but the only weak convergence. The evolution of the em pirical 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://stable.researchseminars.org/talk/LPDD/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Eveliina Peltola (University of Bonn) DTSTART:20200615T133000Z DTEND:20200615T140000Z DTSTAMP:20260404T110829Z UID:LPDD/12 DESCRIPTION:Title: Symmetries and Probabilities in Lattice Models\nby Eveliina Pelto la (University of Bonn) as part of Les probabilités de demain webinar\n\n \nAbstract\nIn statistical physics\, one considers random models of large systems\, whose individual components cannot be studied separately since t here are 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 probability theory. Many interesting models\, such as the so-called Is ing model (describing magnetic material)\, enjoy symmetries that are usefu l when studying features of the model. In particular\, so-called critical lattice models are symmetric with respect to conformal (injective\, holomo rphic) transformations in a certain sense. In this talk\, we discuss how t o make such a concept mathematically precise and how to understand probabi lities of crossing events in such critical models. These questions have le d to interesting discoveries in the mathematics community\, such as the ce lebrated Schramm-Loewner evolution random curves and concepts trying to ma ke sense of quantum field theory rigorously.\n LOCATION:https://stable.researchseminars.org/talk/LPDD/12/ END:VEVENT END:VCALENDAR