A threshold for Poisson behavior of non-stationary product measures

Michael Hochman, Nicolò Paviato

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 $\nu$-almo…