主 题: A Monotone Sinai theorem
报告人: Dr. Terry Soo (Warwick University U.K.)
时 间: 2014-05-19 15:00-16:00
地 点: 北京大学理科一号楼1479（概率论系列报告）
Let X be the space of all bi-infinite sequences of nonnegative integers less than some finite N, and endow X with the shift map T, so that Tx(i) =x(i+1). A self-map f on X is equivariant if f(Tx) = Tf(x), and monotone if f(x)(i) is no greater than x(i). Let mu and nu be product measures on X.Sinai proved that if the entropy of nu is less than mu, then there exists an equivariant map so that push-forward of mu is nu; in joint work with Anthony Quas, we show that if we also assume that the entropy inequality is strict and mu stochastically dominates nu, then Sinai's theorem can be realized via a monotone map.