JournalsaihpdVol. 8, No. 2pp. 159–177

Perfect simulation of the hard disks model by partial rejection sampling

  • Heng Guo

    University of Edinburgh, UK
  • Mark Jerrum

    Queen Mary, University of London, UK
Perfect simulation of the hard disks model by partial rejection sampling cover

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Abstract

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 OO(lognn) rounds, and total time O(n)O(n), where nn is the expected number of disks. The method extends easily to the hard spheres model in d>2d > 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.

Cite this article

Heng Guo, Mark Jerrum, Perfect simulation of the hard disks model by partial rejection sampling. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 8 (2021), no. 2, pp. 159–177

DOI 10.4171/AIHPD/99