Perfect Sampling in Infinite Spin Systems via Strong Spatial Mixing

@article{Anand2022PerfectSI,
  title={Perfect Sampling in Infinite Spin Systems via Strong Spatial Mixing},
  author={Konrad Anand and Mark Jerrum},
  journal={ArXiv},
  year={2022},
  volume={abs/2106.15992}
}
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 runtime is linear in the size of the window. 

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