| Abstract: |
| We prove the Large Deviation Principles for a topologically mixing, one-sided topological Markov shift on a countably infinite number of alphabets which satisfies a strong combinatorial assumption called ``the big images and pre-images property``. More precisely, we assume the existence of a Gibbs measure in the sense of Bowen, and establish the level-2 Large Deviation Principles for the distribution of Birkhoff averages under the Gibbs measure, as well as that of weighted periodic points and iterated pre-images. As an illustration, we apply our results to the Gauss transformation and obtain a global limit theorem on the frequency of digits in the regular continued fraction expansion. |
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