Random Walks on Hyperbolic Groups by Peter Haissinsky

Explore the foundations of random walks on hyperbolic groups in this comprehensive lecture by Peter Haissinsky, part of the "Probabilistic Methods in Negative Curvature" program at the International Centre for Theoretical Sciences. Delve into the intersection of probability theory, ergodic theory, and Gromov hyperbolic groups as Haissinsky introduces key concepts and techniques. Learn about the connections between asymptotic properties of random walks and the large-scale geometry of underlying groups, entropic techniques for studying Poisson boundaries, and Kaimanovich's conditions for equating Poisson and Gromov boundaries. Gain insights into recent developments in applying probabilistic methods to hyperbolic groups, including local limit theorems. This 1-hour 27-minute lecture serves as an essential foundation for understanding the complex interplay between random walks and hyperbolic group structures.