Excited random walk with periodic cookies – Tal Orenshtein

Tal Orenshtein
The Weizmann Institute of Science, Rehovot, Israel
https://sites.google.com/site/talorenshtein314159/

Date(s) : 23/01/2015   iCal
11 h 00 min - 12 h 00 min

We will discuss excited random walk on the integers in elliptic and identically piled environments with periodic cookies.
This is a discrete time process on the integers defined by parameters $p_1,…,p_M$ in $(0,1)$ for some positive integer $M$, where in the $i$-th visit to an integer $z$ the walker moves to $z+1$ with probability $p_{i \mod M}$, and to $z−1$ with probability $1-p_{i \mod M}$. The main result will be discussed is an explicit formula, in terms of $p_1,…,p_M$, for determining recurrence, transience to the left, or transience to the right. As an application one can easily construct transient walks even when the average drift per period is zero.
This is a joint work with Gady Kozma and Igor Shinkar.

 

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