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 29 mai

11h15 - 12h00 : Carlangelo LIVERANI - *Random Walk in Markovian environment.*

12h00 - 12h30 : Marc WOUTS - *A Coarse graining for the Fortuin-Kasteleyn measure in random media.*

12h30 - 14h00 : Déjeuner

14h00 - 16h00 : Enrique ANDJEL - *Mini-cours 1 : Systèmes de particules non-felleriens.*

16h00 - 16h20 : Pause

16h20 - 17h05 : Christophe BAHADORAN - *A generalization of the Derrida-Lebowitz-Speer functional for open asymmetric systems.*

17h05 - 17h35 : Alain CAMANES - *Polymères dirigés et uniforme intégrabilité.*

17h35 - 18h20 : Stefano OLLA - *Microscopic models for heat conduction.*

## Mercredi 30 mai

09h00 - 11h00 : Enrique ANDJEL - *Mini-cours 2 : Systèmes de particules non-felleriens.*

11h00 - 11h20 : Pause

11h20 - 11h50 : Vincent DEVEAUX - *Gibbsian theory for Partially Ordered Models.*

11h50 - 12h35 : Nicolas PETRELIS - *On the localized phase of a copolymer in an emulsion: super-critical percolation regime.*

12h35 - 14h00 : Déjeuner

14h00 - 14h30 : Olivier BERTONCINI - *Metastability and cutoff phenomenon for birth and death chains.*

14h30 - 15h15 : Fraydoun REZAKHANLOU - * Coagulating and Fragmenting Brownian particles.*

## Mini-cours

Enrique ANDJEL (Marseille) Systèmes de particules non-felleriens. La grande majorité des articles sur les systèmes de particules en interaction concernent des processus de Feller. Souvent les méthodes employées ne s'appliquent pas directement aux systèmes non felleriens. Nous parlerons des techniques qui ont été developpées pour surmonter ces difficultés.

## Conférences

Christophe BAHADORAN (Clermont-Ferrand) A generalization of the Derrida-Lebowitz-Speer functional for open asymmetric systems. The DLS functionals describe stationary large deviations of the density profile for TASEP or SSEP with open boundaries, and their non-local structure reflects long-range correlation in nonequilibrium stationary states. They were derived by explicit model-dependent computations. For SSEP a different approach was initiated by Bertini and al, the so-called "macroscopic fluctuation theory", which derives the stationary functional from a dynamical one, and identifies optimal paths. This approach has the advantage of partially extending to other models. In this talk, I will explain a similar derivation for TASEP and more general asymmetric particle systems. In this case the dynamical functional and variational problem are very different because of shocks (including the boundaries).

Olivier BERTONCINI (Rouen) Metastability and cutoff phenomenon for birth and death chains. Metastability is a physical property of some systems to stay for a long time in a non-equilibrium state called metastable stable. In this talk I will describe the behavior of such a system and present the mathematical characterization of this phenomenon. Then I will discuss its relation with the cutoff phenomenon or abrupt convergence to equilibrium, and give conditions for their existence for birth and death chains.

Alain CAMANES (Nantes) Polymères dirigés et uniforme intégrabilité.

Vincent DEVEAUX (Rouen) Gibbsian theory for Partially Ordered Models. We define the notion of Partially Ordered Models that generalize PCA. These measures are defined through Partially Ordered Specifications (POS) in analogy with the statistical mechanics notion of Gibbs measure. We obtain the analogous of Gibbs phase space properties: characterization of extremal measures, criterion of uniqueness, construction and reconstruction starting from single site kernels. We apply this new theory to some well-known PCA.

Carlangelo LIVERANI (Rome 2) Random Walk in Markovian environment. I will present some joint work with D.Dolgopyat and G.Keller on random walks with transition probabilities weakly depending on an environment evolving according to a quite general mixing Markovian evolutions. We prove the CLT for almost all environment histories in all dimensions.

Stefano OLLA (Paris) Microscopic models for heat conduction.

Nicolas PETRELIS (Eurandom) On the localized phase of a copolymer in an emulsion: super-critical percolation regime.

Fraydoun REZAKHANLOU (Berkeley) Coagulating and Fragmenting Brownian particles. Smoluchowski's equation is used to describe the coagulation and fragmentation processes macroscopically. Microscopically clusters of various sizes coalesce to form larger clusters and fragment into smaller clusters. I describe how from a stochastic model of interacting Brownian particles one can derive the Smoluchowski's equation in a scaling limit. This is achieved only if there is no gelation. The main tool is a new correlation bound on the particle distribution. (Joint work with A. M. Hammond and M.R. Yaghouti).

Marc WOUTS (Paris 7) A Coarse graining estimate for the Fortuin-Kasteleyn measure in random media. By the mean of a multi-scale analysis we describe the typical geometrical structure of the clusters under the FK measure in random media. Our result holds in any dimension greater or equal to 2 provided that slab percolation occurs under the annealed measure, which should be the case in the whole supercritical phase. This work extends the one of Pisztora and provides an essential tool for the analysis of the supercritical regime in disordered FK models and in the corresponding disordered Ising and Potts models.