Introduction to (generalized) Gibbs measures

Arnaud Le Ny (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay

These notes have been written to complete a mini-course "Introduction to (generalized) Gibbs measures" given at the universities UFMG (Universidade Federal de Minas Gerais, Belo Horizonte, Brasil) and UFRGS (Universidade Federal do Rio Grande do Sul, Porto Alegre, Brasil) during the first semester 2007. The main goal of the lectures was to describe Gibbs and generalized Gibbs measures on lattices at a rigorous mathematical level, as equilibirum states of systems of a huge number of particles in interaction. In particular, our main message is that although the historical approach based on potentials has been rather successful from a physical point of view, one has to insist on (almost sure) continuity properties of conditional probabilities to get a proper mathematical framework.

Mots clés: Gibbs and generalized Gibbs measures

Domaines: Probabilités [math.PR]

Arnaud Le Ny. Introduction to (generalized) Gibbs measures. 2007. ⟨hal-00194866⟩