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.