Differential Geometry Seminar | 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.

Zoom link：

https://us06web.zoom.us/j/2715345558?pwd=eXRTTExpOVg4ODFYellsNXZVVlZvQT09