The aim of this conference is to bring together mathematicians and physicists working on disordered or random systems, and to discuss recent developments on themes of common interest. Each of the two days is devoted to a specific topic, as described below for the 2001 session.
Time does not allow for oral communications other than the invited lectures. Please bring in preprints and reprints for display.
The `` Rencontre de Physique Statistique'' taking place in Paris 25 and 26 January 2001 welcomes short communications.

Tuesday 23 January: Rapidity of convergence to equilibrium or stationary states

Moderator: Stefano Olla (Cergy-Pontoise)

In problems related to evolution in Physics and Mathematics, the characterization of stationary states is one of the central issues. However, in the applications, it is often essential to estimate the time needed to reach those stationary states. The goal of this meeting is to discuss various recent results on the rapidity of convergence to equilibrium or stationary states in different fields: statistical mechanics, interacting particle systems, deterministic or stochastic dynamical systems and partial differential equations such as the Boltzmann equation.

Speakers: V. Baladi (Orsay), E. Janvresse (Rouen), W. Krauth (ENS Paris), M. Ledoux (Toulouse), C. Liverani (Rome), F. Martinelli (Rome), S. Olla (Cergy-Pontoise), A. Stuart (Warwick), D. Talay (Sophia Antipolis), C. Villani (ENS Lyon).

Titles and abstracts - Schedule

Wednesday 24 January: Coarse graining in statistical mechanics with long range potentials

Moderator: Errico Presutti (Rome)

Kac potentials have been introduced in the 60's to derive the van der Waals theory from statistical mechanics. There is a scaling parameter gamma in the interaction which controls its range (proportional to gamma^-1) and its strength (proportional to gamma^d, d the space dimension). With the works of Kac, Uhlenbeck and Hemmer, [J. Math. Phys. 4, (1963)] and Lebowitz and Penrose, [J. Math. Phys. 7 (1966)] the project was accomplished. It was proved in fact that the limit gamma going to 0 after the infinite volume limit, yields mean field thermodynamics with the Maxwell equal area rule.
More recently the theory has been revisited with the project of working at positive values of gamma, without taking the last limit gamma going to 0, thus studying genuine models of statistical mechanics with finite (even if long) range interactions. The idea is to use perturbative methods regarding gamma as the small parameter and perturbing mean field, which corresponds to gamma = 0.
By extending low temperature techniques and using renormalization group ideas the project has registered several successes, including existence of phase transitions in lattice and continuum models, both classical and quantum; surface tension and Wulff shape; dynamics of interfaces and derivation of motion by curvature (in some scaling limit); metastability and spinodal decomposition. All these and other aspects are currently object of investigation and the research is very active in the field.

Speakers: A. Asselah (Marseille), L. Bertini (Roma), T. Bodineau (Paris), J.L. Lebowitz (Rutgers), O. Penrose (Edinburgh), E. Presutti (Rome), L. Triolo (Roma), M. Zahradník (Prague).

Titles and abstracts - Schedule

The conference is free and open to all. To facilitate local organization, please register.

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