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Annales de l’Institut Henri Poincaré D


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Volume 8, Issue 2, 2021, pp. 159–177
DOI: 10.4171/AIHPD/99

Published online: 2021-03-03

Perfect simulation of the hard disks model by partial rejection sampling

Heng Guo[1] and Mark Jerrum[2]

(1) University of Edinburgh, UK
(2) Queen Mary, University of London, UK

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, 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.

Keywords: Hard disks model, exact sampling, rejection sampling

Guo Heng, Jerrum Mark: Perfect simulation of the hard disks model by partial rejection sampling. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 8 (2021), 159-177. doi: 10.4171/AIHPD/99