Mathematics Colloquium

Poisson-Furstenberg boundaries of random walks

Speaker: Anna Erschler

Location: Warren Weaver Hall 1302

Date: Monday, December 5, 2022, 3:45 p.m.


Poisson boundary is a probability space, defined by a Markov chain;

the origins of this concept go back to the works of Blackwell, Feller and Doob.
Non-triviality of the boundary is equivalent to the existence of non-constant bounded harmonic functions, and related to growth and isoperimetric inequalities of graphs.
We will discuss criteria for triviality and non-triviality of the boundary, methods of complete description of the boundary and applications to asymptotic geometry of the space. I will explain recent progress and discuss fundamental questions that remain open.