Singularity of Furstenberg measure for infinite covolume discrete subroups in higher rank

Homin Lee, Wouter Van LimBeek, Giulio Tiozzo

We consider symmetric random walks on discrete, Zariski-dense subgroups $\Gamma$ of a semisimple Lie group $G$ with Property (T). We prove that if $\Gamma$ has infinite covolume, then the as…