Tel Aviv University 
Dear all,
This week at the Horowitz seminar on Probability, Ergodic Theory and
Dynamical Systems at Tel Aviv University we are happy to have:
Speaker: Gidi Amir, Bar-Ilan University
Title: A continuum of exponents for the rate of escape of random
walks on groups
Date: Monday, January 23
Time: 14:30
Place: Schreiber 309
For every 3/4 ~I beta < 1 we construct a finitely generated group
so that the expected distance of the simple random walk from its
starting point after n steps is n^beta (up to constants). This
answers a question of Vershik, Naor and Peres. In other examples, the
speed exponent can fluctuate between any two values in this interval.
Previous examples were only of exponents of the form 1-1/2^k or 1,
and were based on lamplighter (wreath product) constructions. (Other
than the standard beta=1/2 and beta=1 which are simply diffusive and
ballistic behaviours known for a wide variety of groups) In this
lecture we will describe how a variation of the lamplighter
construction, namely the permutational wreath product, can be used to
get precise bounds on the rate of escape in terms of return
probabilities of the random walk on some Schreier graphs. We will
then show how groups of automorphisms of rooted trees, related to
automata groups, can then be constructed and analyzed to get the
desired rate of escape. This is joint work with Balint Virag of the
University of Toronto. No previous knowledge of automaton groups or
wreath products is assumed.
Best regards,
Seminar webpage:
Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <> 
Announcement from: Ron Peled   <>