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Article Dans Une Revue Geometric And Functional Analysis Année : 2022

Random walks with bounded first moment on finite-volume spaces

Timothée Bénard
  • Fonction : Auteur

Résumé

Let G be a real Lie group, Λ ≤ G a lattice, and Ω = G/Λ. We study the equidistribution properties of the left random walk on Ω induced by a probability measure µ on G. It is assumed that µ has a finite first moment, and that the Zariski closure of the group generated by the support of µ in the adjoint representation is semisimple without compact factors. We show that for every starting point x ∈ Ω, the µ-walk with origin x has no escape of mass, and equidistributes in Cesàro averages toward some homogeneous measure. This extends several fundamental results due to Benoist-Quint and Eskin-Margulis for walks with finite exponential moment.
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Dates et versions

hal-03853360 , version 1 (15-11-2022)

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Timothée Bénard, Nicolas de Saxcé. Random walks with bounded first moment on finite-volume spaces. Geometric And Functional Analysis, 2022, ⟨10.1007/s00039-022-00607-6⟩. ⟨hal-03853360⟩
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