Excited random walks

Excited random walks were introduced in 2003 by I. Benjamini and D. Wilson. The authors asked the following question: what will happen to a simple symmetric random walk (SSRW) on the d-dimensional integer lattice if upon the first visit to every site it received a “push” in, say, the first coordinate direction but on all subsequent visits to the same site it made unbiased steps to its nearest neighbors. Such process is clearly non-markovian. Its properties happen to be very different from those of SSRW. The original model was generalized in various ways but the idea is to consider random processes with jump probabilities which depend on the local time at the current location. In this talk I am planning to give an overview of some of these models and known results and then focus on d=1 where the behavior of excited random walks can be studied in detail via generalized Ray-Knight theorems. Some of the ideas of this approach go back to works of H. Kesten, M.V. Kozlov, and F. Spitzer (1975) on random walks in random environment and of B. Toth (1996) on self-interacting random walks.
Ссылка для подключения:
https://zoom.us/j/93175142429?pwd=VDViRHNOSlZSVUM5ZU03SGZyZy8xQT09
Id: 931-7514-2429 passw=057376