Pressure Inequalities for Gibbs Measures of Countable Markov Shifts

TL;DR

This paper investigates the uniqueness of Gibbs measures in countable Markov shifts with H"older continuous potentials, providing quantitative bounds and convergence rates for approximations by finite subsystems.

Contribution

It offers a new quantification of Gibbs measure uniqueness and convergence rates for countable Markov shifts with locally H"older continuous potentials.

Findings

Quantified the conditions for Gibbs measure uniqueness.

Derived convergence rate bounds for finite subsystem approximations.

Extended results to topologically mixing countable Markov shifts.

Abstract

We provide a quantification of the uniqueness of Gibbs measure for topologically mixing countable Markov shifts with locally H\"older continuous potentials. Corollaries for speed of convergence for approximation by finite subsystems are also given.