BIRS Workshop Lecture Videos

Banff International Research Station Logo

BIRS Workshop Lecture Videos

Relative Gibbs measures and relative equilibrium measures Taati, Siamak

Description

In equilibrium statistical mechanics, the macroscopic states of a system at thermal equilibrium are described by probability measures on the space of microscopic states that maximize pressure. For systems whose microscopic states are symbolic configurations from a subshift, Dobrushin, Lanford and Ruelle showed that under broad conditions, global and local equilibrium conditions are equivalent, that is, "equilibrium measures" are the same as (shift-invariant) "Gibbs measures". I will discuss some variants and generalizations of this theorem, in particular, a broad generalization to systems in contact with a random environment. Some nice symbolic dynamics issues arise. The underlying lattice can be any countable amenable group.

Item Media

Item Citations and Data

Rights

Attribution-NonCommercial-NoDerivatives 4.0 International