Séminaire Gaston Darboux :

Le 23 novembre 2012 à 11:15 - salle 431

Présentée par Tanaka Ryokichi - Tohoku university, Sendai

A global law of large number on nilpotent groups

We discuss about random walks on finitely generated nilpotent groups. As we see, the behaviour of a random walk at infinity is closely related to the Gromov-Hausdorff limit of the groups. We show a large deviation principle for the random walk and see that it gives a version of a (strong) law of large numbers on groups. This describes the point to which the random walk converges. We will also see how the Carnot-Caratheodory metric involves in this limit theorem.