Random Walks on Symmetric Structures

Event date: October 7 - October 11, 2018

    Ori Gurel-Gurevich (The Hebrew University)
    Ohad-Noy Feldheim (The Hebrew University)
    Gideon Amir (Bar Ilan University)



    The study of random walks on Cayley graphs is a central part of modern probability theory. The main questions in this area revolve around the connections between geometric properties of the group and the behavior of a random walk on a the group. Examples of such connections include the relation between return probabilities of the random walk and the spectral radius of the group, its amenability, its isoperimetric profile and its volume growth and the relation between the entropy and rate of escape of the random walk, its Poisson-Furstenberg boundary and its embedding into Hilbert space. Most of these connections cannot be extended to general (non-transitive) graphs. A natural question is what type of symmetry is required from the graph in order for such connections to hold.


    In recent years, a new category, stationary random graphs, emerged. These are random rooted graphs on which the simple random walk is stationary. Such graphs appear naturally in various contexts (e.g. random walk in random environment, uniform infinite planar triangulation). It has been discovered that some of the above mentioned connections carry over from the category of groups to stationary random graphs.


    In this workshop we intend to explore which methods and results can be extended from the realm of groups to stationary random graphs. In doing so we hope to gain better understanding of the factors that determine each random walk behavior, both on stationary random graphs and on Cayley graphs.



    Confirmed Speakers:

    Yuval Peres                Microsoft Research

    Vladas Sidoravicius   NYU Shanghai

    Vadim Kaimanovich    University of Ottawa
    James Lee                  University of Washington
    Tom Hutchcroft           University of Cambridge
    Agelos Georgakopoulos    University of Warwick

    Omer Angel                University of British Columbia
    Balint Virag                 University of Toronto
    Tianyi Zheng              UC San Diego
    Jeremie Brieussel      Université de Montpellier
    Nicolás Matte                  BON ETH Zürich
    Gabor Elek                Alfréd Rényi Institute
    Miklos Abert              Alfréd Rényi Institute