Central limit theorem and law of the iterated logarithm for the linear random walk on the torus

2016/02/11 by Jean−Baptiste Boyer, Boyer, Jean-Baptiste, Jean-Baptiste Boyer
Computer Science · Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Probability (math.PR) #Quantum chaos and dynamical systems #Stochastic processes and statistical mechanics #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1602.03849

openalex publication_date 2016/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let ρ be a probability measure on SL_d(ℤ) and consider the random walk defined by ρ on the torus \mathbbT^d = ℝ^d/ℤ^d. Bourgain, Furmann, Lindenstrauss and Mozes proved that under an assumption on the group generated by the support of ρ, the random walk starting at any irrational point equidistributes in the torus. In this article, we study the central limit theorem and the law of the iterated logarithm for this walk starting at some point having good diophantine properties.

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