A threshold for Poisson behavior of non-stationary product measures

Michael Hochman; Nicolò Paviato

doi:10.1017/etds.2025.10258

A threshold for Poisson behavior of non-stationary product measures

Michael Hochman
, Nicolò Paviato

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let γ_n = O(log^-c n) and let be the infinite product measure whose nth marginal is Bernoulli (1/2 + γ_n). We show that c=1/2 is the threshold, above which v-almost every point is simply Poisson generic in the sense of Peres and Weiss, and below which this can fail. This provides a range in which is singular with respect to the uniform product measure, but v-almost every point is simply Poisson generic.

Original language	English
Pages (from-to)	1009-1019
Number of pages	11
Journal	Ergodic Theory and Dynamical Systems
Volume	46
Issue number	4
DOIs	https://doi.org/10.1017/etds.2025.10258
State	Published - 1 Apr 2026

Bibliographical note

Publisher Copyright:
© The Author(s), 2025. Published by Cambridge University Press.

Keywords

Poisson limit theorem
product measures

Access to Document

10.1017/etds.2025.10258

Cite this

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N2 - Let γn = O(log-c n) and let be the infinite product measure whose nth marginal is Bernoulli (1/2 + γn). We show that c=1/2 is the threshold, above which v-almost every point is simply Poisson generic in the sense of Peres and Weiss, and below which this can fail. This provides a range in which is singular with respect to the uniform product measure, but v-almost every point is simply Poisson generic.

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A threshold for Poisson behavior of non-stationary product measures

Abstract

Bibliographical note

Keywords

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