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 environments Date: Monday, April 29 Time: 14:30 Place: Schreiber 309 Abstract: 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, 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>