Abstract: We will give an introduction to random walks on groups satisfying various types of negative curvature conditions. A simple example is the nearest neighbor random walk on the 4-valent tree, also known as the Cayley graph of the free group on two generators. A typical random walk moves away from the origin at linear speed, and converges to one of the ends of the tree. We will discuss how to generalize this result to more general settings, such as hyperbolic groups, or acylindrical groups. This is joint work with Giulio Tiozzo.
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