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• W2951769645 abstract "The family of pairwise independently determined (PID) systems, i.e. those for which the independent joining is the only self joining with independent 2-marginals, is a class of systems for which the long standing open question by Rokhlin, of whether mixing implies mixing of all orders, has a positive answer. We show that in the class of weakly mixing PID one finds a positive answer for another long-standing open problem, whether the multiple ergodic averages begin{equation*} frac 1 Nsum_{n=0}^{N-1}f_1(T^nx)cdots f_d(T^{dn}x), quad Nto infty, end{equation*} almost surely converge." @default.
• W2951769645 created "2019-06-27" @default.
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• W2951769645 date "2016-12-08" @default.
• W2951769645 modified "2023-10-16" @default.
• W2951769645 title "Almost sure convergence of the multiple ergodic average for certain weakly mixing systems" @default.
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• W2951769645 doi "https://doi.org/10.48550/arxiv.1612.02873" @default.
• W2951769645 hasPublicationYear "2016" @default.
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