A threshold for Poisson behavior of non-stationary product measures
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866908876747571200 |
|---|---|
| author | Hochman, Michael Paviato, Nicolò |
| author_facet | Hochman, Michael Paviato, Nicolò |
| contents | Let $γ_{n}= O (\log^{-c}n)$ and let $ν$ be the infinite product measure whose $n$-th marginal is Bernoulli$(1/2+γ_{n})$. We show that $c=1/2$ is the threshold, above which $ν$-almost every point is simply Poisson generic in the sense of Peres-Weiss, and below which this can fail. This provides a range in which $ν$ is singular with respect to the uniform product measure, but $ν$-almost every point is simply Poisson generic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11423 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A threshold for Poisson behavior of non-stationary product measures Hochman, Michael Paviato, Nicolò Dynamical Systems Probability 60G55, 11K16 (Primary), 37A40, 28A35 (Secondary) Let $γ_{n}= O (\log^{-c}n)$ and let $ν$ be the infinite product measure whose $n$-th marginal is Bernoulli$(1/2+γ_{n})$. We show that $c=1/2$ is the threshold, above which $ν$-almost every point is simply Poisson generic in the sense of Peres-Weiss, and below which this can fail. This provides a range in which $ν$ is singular with respect to the uniform product measure, but $ν$-almost every point is simply Poisson generic. |
| title | A threshold for Poisson behavior of non-stationary product measures |
| topic | Dynamical Systems Probability 60G55, 11K16 (Primary), 37A40, 28A35 (Secondary) |
| url | https://arxiv.org/abs/2501.11423 |