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arXiv · 2301.02841

Level-2 large deviation principle for countable Markov shifts without Gibbs states

Hiroki Takahasi
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Abstract

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 R\'enyi 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 R\'enyi map.

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Hiroki Takahasi. 2023-01-07. Level-2 large deviation principle for countable Markov shifts without Gibbs states. https://doi.org/10.1007/s10955-023-03126-2

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