Abstract
We study skew-products of the form , where is a nonuniformly expanding map on a space , preserving a (possibly singular) probability measure , and is a function. Under mild assumptions on and , we prove that such a map is exponentially mixing and satisfies both the central limit and local limit theorems. These results apply to a random walk related to the Farey sequence, thereby answering a question of Guivarc'h and Raugi [GR, Section 5.3]
Citation
Sébastien Gouëzel. "Local limit theorem for nonuniformly partially hyperbolic skew-products and Farey sequences." Duke Math. J. 147 (2) 193 - 284, 1 April 2009. https://doi.org/10.1215/00127094-2009-011
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