Ober­se­mi­nar "Sto­chas­tik": Se­bas­ti­an Men­te­mei­er (Hil­des­heim), Ran­dom walks on ma­trix (se­mi-)groups

Ort: J3.330

Let d > 1. Let A be a random matrix taking values in one of the following (semi-)groups:

  • GL(d,R), the group of invertible real matrices
  • R> x O(d), the group of similarity matrices
  • M(dxd,R>=), the semi-group of nonnegative matrices

Goal: To study properties of the left random walk (=product of matrices)
Pin  = An *... * A1,
where (An) is a sequence of i.i.d.copies of A; and to study its action on Rd.

I will describe the history of the problem, explain what assumptions are needed to prove limit theorems for Pin and highlight recent research directions; including conditional limit theorems and approximative duality.