2021/11/28 by Timothée Bénard, Bénard, Timothée, Nicolas de Saxcé +1
Computer Science · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Probability (math.PR) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2111.14187
openalex publication_date 2021/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.