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Random Walks on Symmetric Structures
Organizers:

Ori GurelGurevich (The Hebrew University)
OhadNoy 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 PoissonFurstenberg boundary and its embedding into Hilbert space. Most of these connections cannot be extended to general (nontransitive) 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