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arXiv · 1910.09846

Tied-down occupation times of infinite ergodic transformations

Jon. Aaronson·Toru Sera
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Abstract

We prove distributional limit theorems (conditional and integrated) for the occupation times of certain weakly mixing, pointwise dual ergodic transformations at "tied-down" times immediately after "excursions". The limiting random variables include the local times of $p$-stable L\'evy-bridges ($1<p\le 2$) and the transformations involved exhibit "tied-down renewal mixing" properties which refine rational weak mixing. Periodic local limit theorems for Gibbs-Markov and AFU maps are also established.

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Jon. Aaronson, Toru Sera. 2019-10-22. Tied-down occupation times of infinite ergodic transformations. https://arxiv.org/abs/1910.09846

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