Escape of mass for measures invariant under the diagonal group
Presenter
May 13, 2015
Keywords:
- thin subgroup
- discrete subgroups
- SL(n,Z)
- compact orbit
- unimodular lattices
- ergodic measure
- convergence of measure
MSC:
- 20H05
- 20Hxx
- 20-xx
- 37-xx
- 22D40
- 28Dxx
- 43A46
- 43Axx
Abstract
Let A denote the diagonal group in SL(n,R) acting on the space of unimodular lattices in R^n. In this talk I will explain a construction of a sequence of A-invariant ergodic probability measures (supported on compact A-orbits) which converge to the zero measure. In fact the "geometry" of these orbits will be described in some detail.