Perfect sampling from spatial mixing

Abstract

We show that strong spatial mixing with a rate faster than the growth of neighborhood implies the existence of efficient perfect samplers for spin systems. Our new resampling based algorithm bypasses a major barrier of previous work along this line, namely that our algorithm works for general spin systems and does not require additional structures of the problem. In addition, our framework naturally incorporates spatial mixing properties to obtain linear expected running time. Using this new technique, we give the currently best perfect sampling algorithms for colorings in bounded degree graphs and in graphs with sub-exponential neighborhood growth.

Strong spatial mixing for repulsive point processes

“…Perfect sampling algorithms are appealing in practice since no proof of efficiency is needed for a guarantee on their output distribution. For discrete spin systems on graphs of subexponential growth, strong spatial mixing implies the existence of an efficient perfect sampling algorithm [FGY19]. We ask if such an implication holds for Gibbs point processes as well.…”