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:   Multiple excited random walk, excited Mob and leftover

Date:    Monday, April 29

Time:    14:30

Place:   Schreiber 309
We discuss the model of multiple excited random walk on Z, which is a
model of self-interacting random walk on Z which generalizes the
notion of random walk in random environment (in this model the walk
changes the environment as it walks through it). We will survey
results on this model (and higher dimensional analogues) regarding
transience, recurrence and positive speed of such walks, and discuss
some of the techniques involved. In particular we will discuss some
related branching processes and explain how some new observations on
these processes can lead to a 0-1 law for directional transience of
such walks.
We will then discuss new ideas, that allow us to conclude exact
criterions for recurrence, transience and positive speed of such
walks on the "leftover" environments - the environments left over
after a transient walker goes to infinity. For our analysis we
introduce the idea of multiple walkers walking in the same
environment, and show how their movement can be analyzed and used to
understand the leftover environments.
No prior knowledge on excited random walks or random walk in random
environment is assumed.
This is based on joint works with Tal Orenshtein and with Tal
Orenshtein and Noam Berger.
Best regards,


Seminar webpage:

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