Polynomial growth, recurrence and ergodicity for random walks on locally compact groups and homogeneous spaces

Yves Guivarc'H (1) , C. Robinson Edward Raja (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 Statistics and Mathematics Unit

Let G be a locally compact group, E a homogeneous space of G. We discuss the relations between recurrence of a random walk on G or E, ergodicity of the corresponding transformations and polynomial growth of G or E. We consider the special case of linear groups over local fields.

Mots clés: Random walk; ergodicity homogeneous spaces; polynomial growth

Domaines: Probabilités [math.PR]

Yves Guivarc'H, C. Robinson Edward Raja. Polynomial growth, recurrence and ergodicity for random walks on locally compact groups and homogeneous spaces. Workshop on Boundaries, Jun 2009, Graz, Austria. pp.65-74. ⟨hal-00462021v2⟩