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Article Dans Une Revue Ergodic Theory and Dynamical Systems Année : 2012

Recurrence and ergodicity of random walks on linear groups and on homogeneous spaces

Yves Guivarc'H
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C. Robinson Edward Raja
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Résumé

We discuss recurrence and ergodicity properties of random walks and associated skew products for large classes of locally compact groups and homogeneous spaces. In particular we show that a closed subgroup of a product of finitely many linear groups over local fields supports a recurrent random walk if and only if it has at most quadratic growth. We give also a detailed analysis of ergodicity properties for special classes of random walks on homogeneous spaces. The structure of closed subgroups of linear groups over local fields and the properties of group actions with respect to stationary measures play an important role in the proofs.

Dates et versions

hal-00456817 , version 1 (15-02-2010)

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Citer

Yves Guivarc'H, C. Robinson Edward Raja. Recurrence and ergodicity of random walks on linear groups and on homogeneous spaces. Ergodic Theory and Dynamical Systems, 2012, 32 (Part 4), pp.1313-1349. ⟨10.1017/S0143385711000149⟩. ⟨hal-00456817⟩
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