A threshold for Poisson behavior of non-stationary product measures

Le résumé fourni par la source

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.

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