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
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,
Seminar webpage:
Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <> 
Announcement from: Ron Peled   <>