A New Coupling for Sampling from Compact Convex Bodies

A direct route to convergence

Inspired by László Lovász’s work on random walks in convex bodies, we began developing a new coupling for sampling from compact convex bodies. Alongside the construction, we are working on a convergence proof that uses a more elementary argument than the advanced tools used in classical analyses.

A coupling describes two random processes jointly so that their relationship can be studied. For sampling, controlling how the two processes approach one another can help establish how quickly the sampler converges. Our aim is to design a coupling for which this behavior can be analyzed directly, giving a self-contained convergence argument.