Perfect Sampling in Infinite Spin Systems via Strong Spatial Mixing

TL;DR

This paper introduces a straightforward algorithm for perfect sampling of spin system configurations on infinite graphs, leveraging strong spatial mixing and subexponential growth, with linear runtime relative to the sampling window size.

Contribution

The paper proposes a novel, simple perfect sampling algorithm for infinite spin systems under strong spatial mixing conditions, applicable to graphs with subexponential growth.

Findings

Algorithm produces perfect samples efficiently

Run-time is linear in the size of the sampling window

Applicable to infinite graphs with strong spatial mixing

Abstract

We present a simple algorithm that perfectly samples configurations from the unique Gibbs measure of a spin system on a potentially infinite graph $G$. The sampling algorithm assumes strong spatial mixing together with subexponential growth of $G$. It produces a finite window onto a perfect sample from the Gibbs distribution. The run-time is linear in the size of the window.