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 Abstract: For every 3/4 â~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, Ron Seminar webpage: <http://www.math.tau.ac.il/~peledron/Horowitz_seminar/Horowitz_seminar.html> --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Ron Peled <peledron@gmail.com>