Year: 2025
Type: article
Abstract: Let $\gamma _{n}= O (\log ^{-c}n)$ and let $\nu $ be the infinite product measure whose n th marginal is Bernoulli $(1/2+\gamma _{n})$ . We show that $c=1/2$ is the threshold, above which $\nu $ -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 $\nu $ is singular with respect to the uniform product measure, but $\nu $ -almost every point is simply Poisson generic.
Authors: MICHAEL HOCHMAN, NICOLÒ PAVIATO
Institution: Hebrew University of Jerusalem
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
OpenAlex ID: W4416976592