From the 1 of 18 linked papers with an AI index.
18 papers
Strict concavity of the growth indicator function for relatively Anosov groups
Dongryul M. Kim, Hee Oh, Andrew Zimmer
The paper proves that for non‑elementary relatively Anosov subgroups of higher‑rank semisimple Lie groups, the growth indicator function is strictly concave in non‑collinear direct…
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 global shadow lemma for relatively Morse groups in higher rank
Dongryul M. Kim, Hee Oh
Patterson-Sullivan measures encode the distribution of orbits of discrete group actions near the boundary. In this paper, we prove a global shadow lemma for Patterson-Sullivan meas…
Classification of horospherical invariant measures in higher rank: The Full Story
Inhyeok Choi, Dongryul M. Kim
In this paper, we classify horospherical invariant Radon measures for Anosov subgroups of arbitrary semisimple real algebraic groups. This generalizes the works of Burger and Robli…
Non-arithmeticity of length spectra of subgroups of mapping class groups
Inhyeok Choi, Dongryul M. Kim
In this paper, we prove that every non-elementary subgroup of the mapping class group of a surface has non-arithmetic Teichmüller length spectrum. Namely, Teichmüller translation…
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…