Large Deviation Principles for countable Markov shifts

Abstract

We establish the large deviation principle for a topological Markov shift over infinite alphabet which satisfies strong combinatorial assumptions called ``finite irreducibility'' or ``finite primitiveness''. More precisely, we assume the existence of a Gibbs state for a potential $\varphi$ 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 pre-images. The rate function is written with the pressure and the free energy associated with the potential $\varphi$.

26 pages, no figure, Transactions of the American Mathematical Society, to appear

References in corpus (1)

• A multifractal analysis for Stern-Brocot intervals, continued fractions and Diophantine growth rates

Cited by in corpus (1)

• Large Deviation Principle for arithmetic functions in continued fraction expansion