Abstract
We give a survey of recent results on the Poisson-Furstenberg boundaries of random walks on groups, and their applications. We describe sufficient conditions for random walk to have non-trivial boundary, or, on the contrary, to have trivial boundary. We review recent progress in description of the boundary for random walks on various groups, including wreath products. We describe how the Poisson-Furstenberg boundary can be used to obtain lower bounds for the growth function of the groups of intermediate growth. We also discuss relation between properties of the boundary with other asymptotic properties of groups, including isoperimetry and various characteristics of random walks.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
