Renewal theory for random walks on surface groups

Peter Haïssinsky 1, 2 Pierre Mathieu 2 Sebastian Mueller
1 Picard
IMT - Institut de Mathématiques de Toulouse UMR5219
Abstract : We construct a renewal structure for random walks on surface groups. The renewal times are defined as times when the random walks enters a particular type of a cone and never leaves it again. As a consequence, the trajectory of the random walk can be expressed as an "aligned union" of i.i.d. trajectories between the renewal times. Once having established this renewal structure, we prove a central limit theorem for the distance to the origin under exponential moment conditions. Analyticity of the speed and of the asymptotic variance are natural consequences of our approach. Furthermore, our method applies to groups with infinitely many ends and therefore generalizes classic results on central limit theorems on free groups.
Type de document :
Article dans une revue
Ergodic Theory and Dynamical Systems, Cambridge University Press (CUP), 2018, 38 (1), pp.155 -- 179
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https://hal.archives-ouvertes.fr/hal-01228365
Contributeur : Peter Haïssinsky <>
Soumis le : vendredi 13 novembre 2015 - 08:36:22
Dernière modification le : mercredi 12 décembre 2018 - 15:31:06

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  • HAL Id : hal-01228365, version 1
  • ARXIV : 1304.7625

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Peter Haïssinsky, Pierre Mathieu, Sebastian Mueller. Renewal theory for random walks on surface groups. Ergodic Theory and Dynamical Systems, Cambridge University Press (CUP), 2018, 38 (1), pp.155 -- 179. 〈hal-01228365〉

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