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- W2133280196 abstract "Let $(X,mu)$ be a probability space, $G$ a countable amenable group and $(F_n)_n$ a left Folner sequence in $G$. This paper analyzes the non-conventional ergodic averages [frac{1}{|F_n|}sum_{g in F_n}prod_{i=1}^d (f_icirc T_1^gcdots T_i^g)] associated to a commuting tuple of $mu$-preserving actions $T_1$, ..., $T_d:Gcurvearrowright X$ and $f_1$, ..., $f_d in L^infty(mu)$. We prove that these averages always converge in $|cdot|_2$, and that they witness a multiple recurrence phenomenon when $f_1 = ldots = f_d = 1_A$ for a non-negligible set $Asubseteq X$. This proves a conjecture of Bergelson, McCutcheon and Zhang. The proof relies on an adaptation from earlier works of the machinery of sated extensions." @default.
- W2133280196 created "2016-06-24" @default.
- W2133280196 creator A5069962326 @default.
- W2133280196 date "2013-09-17" @default.
- W2133280196 modified "2023-09-27" @default.
- W2133280196 title "Non-conventional ergodic averages for several commuting actions of an amenable group" @default.
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