Save Big on Coursera Plus. 7,000+ courses at $160 off. Limited Time Only! Grab it Learn about detecting stationary measure classes in hyperbolic groups through this mathematics seminar presented by Princeton University's Kunal Chawla at the Institute for Advanced Study. Explore how random walks on hyperbolic groups converge to the boundary and define stationary measures at infinity, with special focus on cocompact fuchsian groups where the boundary is circular. Discover a new geometric family of statistics for determining whether two stationary measures belong to the same measure class, addressing an open question about the relationship between finitely supported random walks and Lebesgue measure absolute continuity.