2021/11/18 by Antoine Goldsborough, Alessandro Sisto, Goldsborough, Antoine +1
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Group Theory (math.GR) #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2111.09837
openalex publication_date 2021/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose the study of Markov chains on groups as a "quasi-isometry invariant" theory that encompasses random walks. In particular, we focus on certain classes of groups acting on hyperbolic spaces including (non-elementary) hyperbolic and relatively hyperbolic groups, acylindrically hyperbolic 3-manifold groups, as well as fundamental groups of certain graphs of groups with edge groups of subexponential growth. For those, we prove a linear progress result and various applications, and these lead to a Central Limit Theorem for random walks on groups quasi-isometric to the ones we consider.