** "Geometry and Analysis on Groups" Research Seminar **

**Time:** 2016.03.15, 15:00–17:00

**Location:** Seminarraum 8, Oskar-Morgenstern-Platz 1, 2.Stock

**Title:** "A spectral theorem for
random walks in Mapping Class Groups: the convergence of the
stretching factors."

**Speaker:** François Dahmani
(Université Joseph Fourier, Grenoble I)

**Abstract:**
In collaboration with C. Horbez, we study the stretching factor of an element obtained by a random walk in a Mapping Class Group. We prove that, under suitable renormalisation along the walk, this sequence converges to a deterministic value, in a way that parallels the convergence of the spectrum of a random product of matrices.