Absolutely continuous Furstenberg measures for finitely-supported random walks
arXiv:2205.11138
Abstract
In this note, we generalise a Bourgain's construction of finitely-supported symmetric measures whose Furstenberg measure has a smooth density from the case of to that of a general simple Lie group. The proof is the same as Bourgain's, except that the use of Fourier series is replaced by harmonic analysis on a maximal compact subgroup.
9 pages