Perfect Simulation of the Hard Disks Model by Partial Rejection Sampling

Authors Heng Guo , Mark Jerrum

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Author Details

Heng Guo
  • School of Informatics, University of Edinburgh, Informatics Forum, Edinburgh, EH8 9AB, United Kingdom.
Mark Jerrum
  • School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London, E1 4NS, United Kingdom.

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Heng Guo and Mark Jerrum. Perfect Simulation of the Hard Disks Model by Partial Rejection Sampling. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 69:1-69:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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(log n) rounds, 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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Randomness, geometry and discrete structures
  • Hard disks model
  • Sampling
  • Markov chains


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