Level-2 Large Deviation Principle for Countable Markov Shifts Without Gibbs States

被引：1

作者：

Takahasi, Hiroki ^{[1
]}

机构：

[1] Keio Univ, Keio Inst Pure & Appl Sci KiPAS, Dept Math, Yokohama 2238522, Japan

来源：

JOURNAL OF STATISTICAL PHYSICS | 2023年 / 190卷 / 07期

关键词：

Thermodynamic formalism; Gibbs state; Large Deviation Principle; periodic points; equidistribution; THERMODYNAMIC FORMALISM; INVARIANT-MEASURES; EQUILIBRIUM MEASURES; ERGODIC-THEORY; MAPS; SYSTEMS; TRANSFORMATIONS; POINTS;

D O I：

10.1007/s10955-023-03126-2

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We consider level-2 large deviations for the one-sided countable full shift without assuming the existence of Bowen's Gibbs state. To deal with non-compact closed sets, we provide a sufficient condition in terms of inducing which ensures the exponential tightness of a sequence of Borel probability measures constructed from periodic configurations. Under this condition we establish the level-2 Large Deviation Principle. We apply our results to the continued fraction expansion of real numbers in [0, 1) generated by the Renyi map, and obtain the level-2 Large Deviation Principle, as well as a weighted equidistribution of a set of quadratic irrationals to equilibrium states of the Renyi map.

引用

页数：25

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