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Perfect Sampling in Infinite Spin Systems via Strong Spatial Mixing (2106.15992v1)
Published 30 Jun 2021 in cs.DS, cs.DM, and math.PR
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.