Description explicite de la frontière de Poisson pour certains groupes de Lie résolubles connexes

Abstract

Let G be a connected solvable Lie group with abelian derived group and μ be a spread out probability measure on G. We give an explicit description of the Poisson boundary in terms of almost sure convergence of the right random walk of law μ. We characterize the Poisson boundary by an integral criterion for some matricial groups.