| Título: | Central Limit Theorem for $\mathbb{Z}_{+}^d$-actions by toral endomorphisms |
| Autores: | Levin, Mordechay |
| Fecha: | 2013-01-04 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: | Peer-reviewed Article |
| Tema: |
Central limit theorem, partially hyperbolic actions, toral endomorphisms 60F15, 37A |
| Descripción: | 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 $s\times s$ 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. |
| Idioma: | Inglés |
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