Videos

Semigroups in semisimple groups, 2

Presenter
February 5, 2015
Keywords:
  • semisimple algebraic groups
  • arithmetic dynamics
  • real semisimple group scheme
  • convex algebraic geometry
  • real algebraic geometry
  • random walks on groups
  • generalizations of the central limit theorem
  • generalizations of the law of large numbers
  • generalizations of the local limit theorem
MSC:
  • 14Pxx
  • 14P10
  • 11Exx
  • 11E10
  • 11-xx
  • 05C81
  • 60F05
  • 60Fxx
Abstract
We will first explain three properties of a Zariski dense subsemigroups of a semisimple real Lie group: - the existence of loxodromic elements, - the convexity and non degeneracy of the limit cone, - the density of the group spanned by the Jordan projection. We will then explain how to deduce from them three limit theorems for a random walk on this semigroup: - the law of large numbers, - the central limit theorem, - the local limit theorem.
Supplementary Materials