30 et 31 mai 2006 - Université de Rouen.

Le but de ces rencontres est de présenter des résultats récents et de discuter des questions nouvelles et ouvertes sur les systèmes de particules et la mécanique statistique.
Elles se composent d'un mini-cours et de conférences.

Mardi 30 mai

11h15 - 12h05 : Jozsef FRITZ - Hyperbolic Scaling Limits.
12h05 - 14h00 : Déjeuner
14h00 - 14h50 : Olivier GARET - Percolation de premier passage et compétition.
14h50 - 15h40 : Régine MARCHAND - Distance chimique et percolation de premier passage.
15h40 - 16h00 : Pause
16h00 - 16h50 : Krishnamurthi RAVISHANKAR - Nucleation and the marked Brownian web.
17h00 - 18h00 : Claudio LANDIM - Mini-cours 1 : Théorème Centrale Limite pour une particule marquée dans l'exclusion simple.

Mercredi 31 mai

09h30 - 11h30 : Claudio LANDIM - Mini-cours 2
11h30 - 11h45 : Pause
11h45 - 12h35 : Enza Orlandi - Gamma convergence for the Allen-Cahn energy with a random external field.
12h35 - 14h00 : Déjeuner
14h00 - 14h50 : Federico BONETTO - Some recent results on the fluctuation theorem.
14h50 - 15h15 : Lamia BELHADJI - Two-Scale Contact Process.
15h15 - 15h30 : Pause
15h30 - 16h30 : Claudio LANDIM - Mini-cours 3 .


Claudio LANDIM (CNRS, Univ. Rouen - IMPA) Théorème Centrale Limite pour une particule marquée dans l'exclusion simple.


Lamia BELHADJI (Univ. Rouen) Two-Scale Contact Process. In this talk, we investigate a generalization of the contact process in which interactions occur at microscopic level and mesoscopic level. The superposition of two interaction levels induces two birth rates, called within and outside birth rates, respectively. We study the effect of patchiness, defined as the ratio of the mesoscopic scale over the microscopic scale, on the survival probability of the particle system. We find that particles are more likely to spread out as patchiness increases, even if the outside birth rate decreases significantly with the square size. (Joint work with Nicolas Lanchier)

Federico BONETTO (Georgia Institute of Technology) Some recent results on the fluctuation theorem. Fluctuations of the entropy production in non equilibrium statistical systems have been investigated in analytical, numerical and experimental works due to the Fluctuation Theorem. This thoerem predict a symmetry for the large fluctuation functional of the entropy production that many believe to be valid well beyond the range of validity of the hypotheses under which one can obtain a rigorous proof. Some recent numerical simulations on deterministic systems with singularities or stochastic systems gave rise to questions on the applicability and form of the Fluctuation Theorem. I will present and discuss some of these system with relevance for future extensions.

Jozsef FRITZ (TU Budapest) Hyperbolic Scaling Limits. Several classes of microscopic models are available, a brief overview of models is presented with a particular interest in the case of two-component systems. The Ginzburg-Landau category is certainly the most interesting from a physical point of view, therefore the related technical difficulties are also considerable. Lattice gas models with a finite or countable individual state space are mixtures of zero range, interacting exclusion or cellular automata models. We are going to discuss the roles of the Lax entropy inequality, compensated compactness, and relaxation schemes in the materialization of the hydrodynamic limit. Due to some recent results of PDE theory, systems with a single conservation law are relatively easy to handle; the case of two macroscopic equations is more difficult.

Olivier GARET (Univ. Orléans) Percolation de premier passage et compétition. Il y a un peu moins de dix ans, Häggström et Pemantle ont remarqué que la percolation de premier passage permettait de modéliser des phénomènes de compétition entre espèces, suscitant aujourd'hui une importante littérature. Le but de l'exposé est de présenter ces problèmes et de donner un aperçu de l'état de l'art.

Régine MARCHAND (IES, Nancy) Distance chimique et percolation de premier passage. Dans la percolation de Bernoulli surcritique, la distance chimique est la longueur du plus court chemin ouvert entre deux points d'un même amas de percolation. On peut la voir comme une distance aléatoire généralisant la percolation de premier passage. Le but de l'exposé est de présenter les résultats de convergence qu'on obtient dans ce cadre : résultat de forme asymptotique et inégalité de grandes déviations.

Enza ORLANDI (Rome 3) Gamma convergence for the Allen-Cahn energy with a random external field.

Krishnamurthi RAVISHANKAR (SUNY - New Paltz) Nucleation and the marked Brownian web. This talk will describe recent work in collaboration with L.R.G. Fontes, C.M. Newman and M. Isopi.
Coarsening on a one-dimensional lattice is described by the voter model or equivalently by coalescing (or annihilating) random walks representing the evolving boundaries between regions of constant color and by backward (in time) coalescing random walks corresponding to color genealogies. Asympotics for large time and space on the lattice are described via a continuum space-time voter model whose boundary motion is expressed by the Brownian web (BW) of coalescing forward Brownian motions. In this talk, we consider how small noise in the voter model, corresponding to the nucleation of randomly colored regions, can be treated in the continuum limit. We present a full construction of the continuum noisy voter model (CNVM) as a random quasicoloring of two-dimensional space time and derive some of its properties. Our construction is based on a Poisson marking of the backward BW within the double (i.e., forward and backward) BW. We will also discuss on going work on nucleation at the boundaries.