Densité d’orbites d’actions de groupes linéaires et propriétés d’équidistribution de marches aléatoires

Jean-Pierre Conze () and Yves Guivarc’h ()
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Jean-Pierre Conze: Université de Rennes 1, Institut de recherche mathématique de Rennes
Yves Guivarc’h: Université de Rennes 1, Institut de recherche mathématique de Rennes

A chapter in Rigidity in Dynamics and Geometry, 2002, pp 39-76 from Springer

Abstract: Abstract We consider a subgroup Γ of the linear group G = Sl(d, ℝ), the unipotent subgroup N of upper triangular matrices and the subgroup A of positive diagonal matrices. The subgroup Γ is supposed to be discrete and “non-elementary”. Using various notions of limit points for Γ we study the density of orbits of Γ in canonically defined Γ-invariant closed subsets of ℝ d , or its wedge products. The closely related situation, where N or A acts on Γ\G is also considered. The method is based on equidistribution properties of random walks on ℝ d or G/N.

Date: 2002
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DOI: 10.1007/978-3-662-04743-9_3

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