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Fast Mixing Random Walks and Regularity of Incompressible Vector Fields (1611.09252v1)
Published 23 Nov 2016 in stat.CO and math.PR
Abstract: We show sufficient conditions under which the \textsc{BallWalk} algorithm mixes fast in a bounded connected subset of $\Realn$. In particular, we show fast mixing if the space is the transformation of a convex space under a smooth incompressible flow. Construction of such smooth flows is in turn reduced to the study of the regularity of the solution of the Dirichlet problem for Laplace's equation.
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