Furstenberg boundary

The Furstenberg boundary is a concept in probability theory and dynamical systems, particularly in the study of random walks on groups and homogeneous spaces. Named after the mathematician Herbert Furstenberg, this boundary provides a way to understand the asymptotic behavior of random walks by relating them to geometric structures. In more detail, the Furstenberg boundary can be defined in the context of a probability measure on a group, often a non-abelian group.