Semigroups in semisimple groups
Introductory Workshop: Geometric and Arithmetic Aspects of Homogeneous Dynamics February 02, 2015 - February 06, 2015
Location: MSRI: Simons Auditorium
Primary Mathematics Subject Classification No Primary AMS MSC Secondary Mathematics Subject Classification No Secondary AMS MSC
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.
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