题   目: Rapid mixing for random walks on nilmanifolds

报告人: Minsung Kim (浦项科技大学)

时间地点: 数学学院新楼 308，5月12日（周二） 15:00-16:00

摘   要：In chaotic systems, the mixing property is known for the fast decay of correlation. It is called rapid mixing if the correlation function decays super-polynomially. The mixing mechanism for hyperbolic systems and its compact group extensions were studied by Dolgopyat in a series of his papers in the late 90s'.

In this talk, we prove rapid mixing for almost all random walks generated by $m\geq 2$ translations on an arbitrary nilmanifold. For several classical classes of nilmanifolds, we show m = 2 suffices. This provides a partial answer to the question raised in the work of Dolgopyat ('02) about the prevalence of rapid mixing for random walks on homogeneous spaces.