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.
PARTICIPANTS
Omer Angel  University of British Columbia 
Jeremie Brieussel  Université de Montpellier 
Gabor Elek  Alfréd Rényi Institute 
Yair Hartman  Ben Gurion University 
Tom Hutchcroft  University of Cambridge 
Vadim Kaimanovich  University of Ottawa 
James Lee  University of Washington 
Alex Lubotzky  Hebrew University of Jerusalem 
Nicolás Matte Bon  ETH Zürich 
Yuval Peres  Microsoft Research 
Doron Puder  Tel Aviv University 
Vladas Sidoravicius  NYU Shanghai 
Romain Tessera  Université ParisSud 
Ariel Yadin  Ben Gurion University 
Dominic Yeo  Technion 