TY - JOUR
T1 - A threshold for Poisson behavior of non-stationary product measures
AU - Hochman, Michael
AU - Paviato, Nicolò
N1 - Publisher Copyright:
© The Author(s), 2025. Published by Cambridge University Press.
PY - 2025
Y1 - 2025
N2 - Let γn = O(log−c n) and let ν be the infinite product measure whose nth marginal is Bernoulli (1/2 + γn). We show that c = 1/2 is the threshold, above which ν-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 ν is singular with respect to the uniform product measure, but ν-almost every point is simply Poisson generic.
AB - Let γn = O(log−c n) and let ν be the infinite product measure whose nth marginal is Bernoulli (1/2 + γn). We show that c = 1/2 is the threshold, above which ν-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 ν is singular with respect to the uniform product measure, but ν-almost every point is simply Poisson generic.
KW - Poisson limit theorem
KW - product measures
UR - https://www.scopus.com/pages/publications/105024248447
U2 - 10.1017/etds.2025.10258
DO - 10.1017/etds.2025.10258
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AN - SCOPUS:105024248447
SN - 0143-3857
JO - Ergodic Theory and Dynamical Systems
JF - Ergodic Theory and Dynamical Systems
ER -