F. Maucourant | Searcharxiv

arXiv2005

Homogeneous asymptotic limits of haar measures of semisimple linear groups and their lattices

We show that Haar measures of connected semisimple groups, embedded via a representation into a matrix space, have a homogeneous asymptotic limit when viewed from far away and appropriately rescaled. This is still true if the Haar measure of the semisimple group is replaced by the Haar measure of a irreducible lattice of the group, and the asymptotic measure is the same. In the case of an almost simple group of rank greater than 2, a remainder term in obtained. This extends and precises anterior results of Duke, Rudnick and Sarnak, and Eskin-McMullen in the case of a group variety.

math.RT↗

arXiv2004

Proximality and equidistribution on the Furstenberg boundary

Let G be a connected semisimple Lie group with finite center and without compact factors, P a minimal parabolic subgroup of G, and Γa lattice in G. We prove that every Γ-orbits in the Furstenberg boundary G/P is equidistributed for the averages over Riemannian balls. The proof is based on the proximality of the action of Γon G/P.

math.DS↗