Topological pressure and the variational principle for actions of sofic groups

Abstract

In this paper, we introduce topological pressure for continuous actions of countable sofic groups on compact metrizable spaces. This generalizes the classical topological pressure for continuous actions of countable amenable groups on such spaces. We also establish the variational principle for topological pressure in this sofic context.

arXiv comment28 pages. Minor changes. Title changed. To appear in Ergod. Th. Dynam. Sys