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arXiv · 2403.02658

Large deviations for occupation and waiting times of infinite ergodic transformations

Toru Sera
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Abstract

We establish large deviation estimates related to the Darling--Kac theorem and generalized arcsine laws for occupation and waiting times of ergodic transformations preserving an infinite measure, such as non-uniformly expanding interval maps with indifferent fixed points. For the proof, we imitate the study of generalized arcsine laws for occupation times of one-dimensional diffusion processes and adopt a method of double Laplace transform.

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Toru Sera. 2024-03-05. Large deviations for occupation and waiting times of infinite ergodic transformations. https://doi.org/10.1017/etds.2025.10246

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