Rapid mixing for random walks on nilmanifolds

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 ≥ 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.

This is joint work with Dmitry Dolgopyat and Spencer Durham.