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Семинар Добрушинской математической лаборатории ИППИ РАН

 

 Семинар Добрушинской математической лаборатории ИППИ РАН

30 июня, вторник, 16:00 пройдет в режиме онлайн-конференции

на платформе Zoom.

Elena Kosygina (City Uni of New York): Excited random walks

Abstract:
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

26.06.2020 | Комеч Сергей Александрович
 

 

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