Math Seminars
Y. Guivarc'h
(Rennes I)
On the spectrum of a Zariski dense subgroup of a semi-simple group and some dynamical applications
We consider a semi-simple real Lie group G , a Zariski-dense subsemigroup T of G. We describe a fullness property of the "spectrum" of T , and we develop some dynamical consequences: The central limit theorem for a random walk on T; the structure of some T-orbit closures in a vector space V if T is contained in GL(V); The calculation of the algebraic hull for a random walk on T.