## Abstract

In this paper we prove the central limit theorem for the following multisequence where f is a Hölder's continue function, A_{1},...,A_{d} are s×s partially hyperbolic commuting integer matrices, and x is a uniformly distributed random variable in [0,1]^{s}. Then we prove the functional central limit theorem, and the almost sure central limit theorem. The main tool is the S-unit theorem.

Original language | English |
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Journal | Electronic Journal of Probability |

Volume | 18 |

DOIs | |

State | Published - 11 Mar 2013 |

## Keywords

- Central limit theorem
- Partially hyperbolic actions
- Toral endomorphisms

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