Fast Mixing Random Walks and Regularity of Incompressible Vector Fields

Abstract

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.

References in corpus (2)

• Hit-and-Run for Sampling and Planning in Non-Convex Spaces
• Thin Partitions: Isoperimetric Inequalities and Sampling Algorithms for some Nonconvex Families