Probability Seminar: Sebastián Barbieri Lemp

The Dobrushin-Lanford-Ruelle theorem gives sufficient
conditions on sets of configurations on the d-dimensional lattice so
that (1) every measure which maximizes the topological pressure is a
Gibbs measure and (2) every Gibbs measure maximizes the topological
pressure. In this talk we shall discuss a generalization of this theorem
in several directions: the lattice is now an arbitrary countable
amenable group, we permit the existence of a random environment and
consider measures that project onto it, and we relax the required
conditions of (1) to a much larger class of dynamical systems. We shall
also present a few applications of this theorem.
 

 

This is joint work with Ricardo Gómez-Aíza, Brian Marcus and Siamak Taati.