6 papers · 1 filter
Measurable boundary maps and Patterson--Sullivan measures for non-Borel Anosov groups on the Furstenberg boundary
Dongryul M. Kim, Andrew Zimmer
In this paper we develop a theory for Patterson--Sullivan measures for non-Borel Anosov groups on the Furstenberg boundary. Previously, such a theory has been successfully develope…
Vector-valued horofunction boundaries and Patterson--Sullivan measures
Dongryul M. Kim, Andrew Zimmer
In higher rank, there is a well-studied theory of Patterson--Sullivan measures supported on partial flag manifolds. However, establishing the existence and uniqueness of such measu…
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…
The structure of relatively hyperbolic groups in convex real projective geometry
Mitul Islam, Andrew Zimmer
In this paper we prove a general structure theorem for relatively hyperbolic groups (with arbitrary peripheral subgroups) acting naive convex co-compactly on properly convex domain…