Chiranjib Mukherjee
University of Münster
March 24, 2025
Randomized geodesic flow: Motivated by Gromov’s geodesic flow problem on hyperbolic groups $G$, we develop an analog using bi-infinite random walks. This leads to a notion of a harmonic analog of the Bowen-Margulis-Sullivan measure on the double-boundary. We provide three different but related constructions of this measure: 1) by moving the base-point along a quasigeodesic ray 2) by moving the base-point along random walk trajectories 3) directly as a push-forward under the boundary map to the double boundary of a measure inherited from studying all bi-infinite random walk trajectories (with no restriction on base-point). Joint work with Luzie Kupffer and Mahan Mj.
University of Münster
March 24, 2025
Randomized geodesic flow: Motivated by Gromov’s geodesic flow problem on hyperbolic groups $G$, we develop an analog using bi-infinite random walks. This leads to a notion of a harmonic analog of the Bowen-Margulis-Sullivan measure on the double-boundary. We provide three different but related constructions of this measure: 1) by moving the base-point along a quasigeodesic ray 2) by moving the base-point along random walk trajectories 3) directly as a push-forward under the boundary map to the double boundary of a measure inherited from studying all bi-infinite random walk trajectories (with no restriction on base-point). Joint work with Luzie Kupffer and Mahan Mj.