MMOnline – Информационный портал о мехмате МГУ

11 марта 2004 года (четверг) в 15:40 в конференц-зале НМУ, Б. Власьевский, 11 состоится очередная лекция семинара Глобус "Random walks along orbits of chaotic maps". Лектор - Вадим Калошин (Caltech, IAS и AIM).

Let f: T^d -> T^d be a measure preserving map of a d-dimensional torus T^d with a smooth measure \mu. For example, the "cat" map given by the matrix
(2 1)
(1 1)
and the Lebesgue measure. Let p: T^d -> (0,1) be a smooth (random environment) function. Consider a random walk. A point x\in T^d jumps to the image fx with probability p(x) and into the preimage f^{-1}x with probability 1-p(x). We are interested in distribution of a point after a large time. Strangely enough if f is chaotic and p generic random walks of x become nonrandom. Namely, with probability arbitrary close to 1 position of image of point x after a long time is located in a set of arbitrary small measure on T^d. In other words, distribution of image of x is getting strongly localized as time increases. This is related to Sinai-Golosov localization of random walks in random environment. Other aspects will be discussed too. This is a joint work with Ya.G.Sinai.

Московское Математическое Общество