A Large deviations principle at zero temperature for stationary Markov equilibrium states on countable Markov shifts
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866910484162150400 |
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| author | Vargas, Victor |
| author_facet | Vargas, Victor |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_04619 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Large deviations principle at zero temperature for stationary Markov equilibrium states on countable Markov shifts Vargas, Victor Dynamical Systems Mathematical Physics Probability 28Dxx, 37Axx, 60Jxx 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. |
| title | A Large deviations principle at zero temperature for stationary Markov equilibrium states on countable Markov shifts |
| topic | Dynamical Systems Mathematical Physics Probability 28Dxx, 37Axx, 60Jxx |
| url | https://arxiv.org/abs/2311.04619 |