Limit theorems on nilpotent Lie groups

Abstract:

I will present limit theorems for random walks on nilpotent Lie groups, obtained in a recent work with Emmanuel Breuillard. Most works on the topic assumed the step distribution of the walk to be centered in the abelianization of the group. Our main contribution is to authorize non-centered step distributions. In this case, new phenomena emerge: the large-scale geometry of the walk depends on the increment average, and the limit measure in the central limit theorem may not have full support in the ambient group.

About the speaker

I am a postdoctoral researcher at the Warwick Mathematics Institute in the UK. I am interested in random walks on Lie groups or their quotient by a discrete subgroup. The mathematical tools involved come from Probability Theory, Dynamical Systems, and Lie Group Theory.