We show sufficient conditions under which the \textsc{ BallWalk} algorithm mixes fast in a bounded connected subset of $\Real^n$. 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.
Categories: stat.CO math.PR