# Perfect Sampling in Infinite Spin Systems via Strong Spatial Mixing

arXiv: https://arxiv.org/abs/2106.15992 · HTML: https://mlsanity.com/paper/2106.15992/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jun 2021.

## Built on by (most cited first, 2 of 2)

- [Perfect Sampling from Pairwise Comparisons](https://mlsanity.com/paper/2211.12868/) (2022)
- [Learning mathsfAC0 under Locally Sampleable Graphical Models](https://mlsanity.com/paper/2607.08303/) (2026)

## Abstract (arXiv)

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.