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- W2016264966 abstract "In this paper we prove the central limit theorem for the following multisequence $$sum_{n_1=1}^{N_1} ... sum_{n_d=1}^{N_d} f(A_1^{n_1}...A_d^{n_d} {bf x} )$$ where $f$ is a Hölder's continue function, $A_1,ldots,A_d$ are $stimes s$ partially hyperbolic commuting integer matrices, and $bf x$ is a uniformly distributed random variable in $[0,1]^s$. Next we prove the functional central limit theorem, and the almost sure central limit theorem. The main tool is the $S$-unit theorem." @default.
- W2016264966 created "2016-06-24" @default.
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- W2016264966 date "2013-01-01" @default.
- W2016264966 modified "2023-09-23" @default.
- W2016264966 title "Central Limit Theorem for $mathbb{Z}_{+}^d$-actions by toral endomorphisms" @default.
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- W2016264966 doi "https://doi.org/10.1214/ejp.v18-1904" @default.
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