LARGE DEVIATION PRINCIPLES FOR COUNTABLE MARKOV SHIFTS

被引：6

作者：

Takahasi, Hiroki ^{[1
]}

机构：

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

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2019年 / 372卷 / 11期

关键词：

THERMODYNAMIC FORMALISM; EQUILIBRIUM STATES;

D O I：

10.1090/tran/7829

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We establish the large deviation principle for a topological Markov shift over infinite alphabet which satisfies strong connectivity assumptions called "finite irreducibility" or "finite primitiveness". More precisely, we assume the existence of a Gibbs state for a potential phi in the sense of Bowen, and prove the level-2 large deviation principles for the distribution of empirical means under the Gibbs state, as well as that of weighted periodic points and iterated preimages. The rate function is written with the pressure and the free energy associated with the potential phi.

引用

页码：7831 / 7855

页数：25

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