Perfect simulation of the hard disks model by partial rejection sampling
Annales de l’Institut Henri Poincaré D, Tome 8 (2021) no. 2, pp. 159-177.
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We present a perfect simulation of the hard disks model via the partial rejection sampling method. Provided the density of disks is not too high, the method produces exact samples in O(logn) rounds, and total time O(n), where n is the expected number of disks. The method extends easily to the hard spheres model in d>2 dimensions. In order to apply the partial rejection method to this continuous setting, we provide an alternative perspective of its correctness and run-time analysis that is valid for general state spaces.

Accepté le :
Publié le :
DOI : 10.4171/aihpd/99
Classification : 82-XX, 60-XX, 68-XX
Mots-clés : Hard disks model, exact sampling, rejection sampling 
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Guo, Heng; Jerrum, Mark. Perfect simulation of the hard disks model by partial rejection sampling. Annales de l’Institut Henri Poincaré D, Tome 8 (2021) no. 2, pp. 159-177. doi : 10.4171/aihpd/99. https://www.numdam.org/articles/10.4171/aihpd/99/
  • Jerrum, Mark Fundamentals of partial rejection sampling, Probability Surveys, Volume 21 (2024) no. none | DOI:10.1214/24-ps29
  • Michelen, Marcus; Perkins, Will Strong Spatial Mixing for Repulsive Point Processes, Journal of Statistical Physics, Volume 189 (2022) no. 1 | DOI:10.1007/s10955-022-02969-5
  • Feng, Weiming; Guo, Heng; Yin, Yitong Perfect sampling from spatial mixing, Random Structures Algorithms, Volume 61 (2022) no. 4, p. 678 | DOI:10.1002/rsa.21079
  • Helmuth, Tyler; Perkins, Will; Petti, Samantha Correlation decay for hard spheres via Markov chains, The Annals of Applied Probability, Volume 32 (2022) no. 3 | DOI:10.1214/21-aap1728

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