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Perfect Sampling in Infinite Spin Systems via Strong Spatial Mixing
Konrad Anand, Mark Jerrum · 2021-06-30 · via math.PR updates on arXiv.org

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.

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