Higher order return times for $\phi$-mixing measures

Nicolai T A Haydn; Gin Park

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arXiv · 2510.14116

Higher order return times for $\phi$-mixing measures

Nicolai T A Haydn·Gin Park

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Abstract

In this paper we consider $\phi$-mixing measures and show that the limiting return times distribution is compound Poisson distribution as the target sets shrink to a zero measure set. The approach we use generalises a method given by Galves and Schmitt in 1997 for the first entry time to higher orders.

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Nicolai T A Haydn, Gin Park. 2025-10-15. Higher order return times for $\phi$-mixing measures. https://arxiv.org/abs/2510.14116

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