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SHEPI
Mars 2011
Jeudi 10 (salle 05) 11h-12h30 : Giambatista Giacomin Around the Kuramoto synchronization model. I will present some results on the long time behavior of a class of models that can be viewed as perturbations of the Kuramoto synchronization model. I will discuss the relevance of these results for modeling in biological sciences and from the standpoint of nonequibrium statistical mechanics. 14h : Kay Kirkpatrick Bose-Einstein condensation, the nonlinear Schrodinger equation, and probabilistic connections. Near absolute zero, a gas of quantum particles can condense into an unusual state of matter, called Bose-Einstein condensation, that behaves like a giant quantum particle and is modeled macroscopically by the cubic nonlinear Schrodinger equation (NLS). I'll describe the NLS and its connections to probability, including its derivation from interacting particle systems (joint work with B. Schlein and G. Staffilani), and its phase transition in the high-dimensional discrete setting (recent work with Sourav Chatterjee).
Mai 2011
25 et 26 mai (Rouen) Rencontres de probabilités 2011 Page web
Juin 2011
Jeudi 09 (salle 05, IHP) 11h-12h30 : David Ruelle A mechanical model for Fourier's law of heat conduction. 14h : Ivan Corwin Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions We consider the solution of the stochastic heat equation with multiplicative noise and delta function initial condition whose logarithm, with appropriate normalizations, is the free energy of the continuum directed polymer, or the solution of the Kardar-Parisi-Zhang equation with narrow wedge initial conditions. We prove explicit formulas for the one-dimensional marginal distributions -- the crossover distributions -- which interpolate between a standard Gaussian distribution (small time) and the GUE Tracy-Widom distribution (large time). The proof is via a rigorous steepest descent analysis of the Tracy-Widom formula for the asymmetric simple exclusion with anti-shock initial data, which is shown to converge to the continuum equations in an appropriate weakly asymmetric limit. The limit also describes the crossover behaviour between the symmetric and asymmetric exclusion processes.
Décembre 2011
Jeudi 08 (salle 201, IHP) 11h-12h30 : Ellen Saada A shape theorem for an epidemic model in dimension $d\ge 3$. This is a joint work with E. D. Andjel and N. Chabot. We prove a shape theorem for the set of infected individuals in a spatial epidemic model with 3 states (susceptible-infected-recovered) on $\Z^d$, $d\ge 3$, when there is no extinction of the infection. For this, we derive percolation estimates (using dynamic renormalization techniques) for a locally dependent random graph in correspondence with the epidemic model. 14h-17h : Geoffrey Grimmett Lipschitz percolation