Special Session 21

Probability and Statistical Mechanics

Organizers: Alessandra Bianchi (University of Padua, Italy), Alessandra Faggionato (University of Rome “La Sapienza”, Italy), Hubert Lacoin (IMPA, Brazil)

MSC codes: 60K35, 82CXX, 60FXX

Description:

The goal of the proposed session is to present recent developments in the field of interacting particle systems and disorder systems, with emphasis on the derivation of macroscopic limits and behavior, and on the characterization of critical phenomena. By gathering contributions across probability theory and statistical mechanics, the session aims to highlight the interplay between randomness, interaction, and geometry, and to shed light on the emergence of macroscopic collective phenomena and on the universality of certain scaling limits. In this general framework, a central problem concerns the characterization of the behavior of random dynamics in inhomogeneous or disordered environments, where random structures interact non-trivially with the evolution of the system. Phenomena such as localization, anomalous transport and metastability, arise naturally in these stochastic dynamics, and examples include random conductance systems, random polymers, interacting particle systems on random structure, and stochastic interface dynamics. A common central objective in all these systems is the derivation and characterization of a large-scale behavior which encodes universal features of the underlying stochastic evolution. Tools such as entropy and relative entropy methods, large deviation techniques, coupling constructions and martingale approaches, have been developed in order to control rare events and establish convergence to a proper scaling limit. The invited speakers will enter into the subject by presenting new analytical tools, rigorous results, and open problems that drive the current research on the area of random interacting dynamics.