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: Yuval Peres, Microsoft Research Title: Balanced self-interacting random walks Date: Monday, December 24 Time: 14:30 Place: Schreiber 309 Abstract: It is well known that a random walk in d>2 dimensions where the steps are i.i.d. mean zero and fully supported (not restricted to a hyperplane), is transient. In a recent elegant paper, Benjamini, Kozma and Schapira (2011) asked if we still must have transience when each step is chosen from either mu_1 or mu_2 based on the past, where mu_1 and mu_2 are fully supported mean zero distributions in dimension d>2. (e.g. we could use mu_1 if the current state has been visited before, and mu_2 otherwise), We answer their question, and show the answer can change when we have three measures instead of two. To prove this, we will adapt the classical techniques of Lyapunov functions and excessive measures to this setting. No prior familiarity with these methods will be assumed, and they will be explained in the talk. Many open problems remain in this area, even in two dimensions. Lecture based on joint work with Serguei Popov (Campinas, Brazil) and Perla Sousi (Cambridge, UK). 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@post.tau.ac.il>