A Large deviations principle at zero temperature for stationary Markov equilibrium states on countable Markov shifts

Victor Vargas

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arXiv · 2311.04619

A Large deviations principle at zero temperature for stationary Markov equilibrium states on countable Markov shifts

Victor Vargas

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Abstract

Consider a topologically transitive unilateral countable Markov shift $Σ$, a locally constant potential $ϕ: Σ\to \mathbb{R}$ satisfying suitable conditions, and assume that $μ_t$ is the unique stationary Markov equilibrium state associated to the potential $tϕ$ for each $t \geq 1$. In this paper we prove a first level large deviations principle at zero temperature for the family of equilibrium states $(μ_t)_{t \geq 1}$ and we extend the result to the setting of bilateral countable Markov shifts.

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Victor Vargas. 2024-06-13. A Large deviations principle at zero temperature for stationary Markov equilibrium states on countable Markov shifts. https://arxiv.org/abs/2311.04619

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