4 papers · 1 filter
Determining subgroups via stationary measures
Dongryul M. Kim, Andrew Zimmer
In this paper, we consider random walks on the isometry groups of general metric spaces. Under some mild conditions, we show that if two non-elementary random walks on a discrete s…
A note on the singularity conjecture for infinite covolume discrete subgroups
Dongryul M. Kim, Andrew Zimmer
We consider random walks on semisimple Lie groups where the support of the step distribution generates (as a group) a Zariski dense discrete subgroup of infinite covolume. When the…
Rigidity for Patterson--Sullivan systems with applications to random walks and entropy rigidity
Dongryul M. Kim, Andrew Zimmer
In this paper we introduce Patterson--Sullivan systems, which consist of a group action on a compact metrizable space and a quasi-invariant measure which behaves like a classical P…
Weakly holomorphic homogeneous regular manifolds
Andrew Zimmer
We introduce a class of complex manifolds which we call weakly holomorphic homogeneous regular manifolds (wHHR) manifolds. As the name suggests, this class contains the so-called h…