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Simulating the component counts of combinatorial structures

Author

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  • Arratia, Richard
  • Barbour, A.D.
  • Ewens, W.J.
  • Tavaré, Simon

Abstract

This article describes and compares methods for simulating the component counts of random logarithmic combinatorial structures such as permutations and mappings. We exploit the Feller coupling for simulating permutations to provide a very fast method for simulating logarithmic assemblies more generally. For logarithmic multisets and selections, this approach is replaced by an acceptance/rejection method based on a particular conditioning relationship that represents the distribution of the combinatorial structure as that of independent random variables conditioned on a weighted sum. We show how to improve its acceptance rate. We illustrate the method by estimating the probability that a random mapping has no repeated component sizes, and establish the asymptotic distribution of the difference between the number of components and the number of distinct component sizes for a very general class of logarithmic structures.

Suggested Citation

  • Arratia, Richard & Barbour, A.D. & Ewens, W.J. & Tavaré, Simon, 2018. "Simulating the component counts of combinatorial structures," Theoretical Population Biology, Elsevier, vol. 122(C), pages 5-11.
    • Handle: RePEc:eee:thpobi:v:122:y:2018:i:c:p:5-11
    DOI: 10.1016/j.tpb.2018.02.002
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    References listed on IDEAS

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    1. Joyce, Paul & Tavaré, Simon, 1987. "Cycles, permutations and the structure of the yule process with immigration," Stochastic Processes and their Applications, Elsevier, vol. 25, pages 309-314.
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    Cited by:

    1. da Silva, Poly H. & Jamshidpey, Arash & Tavaré, Simon, 2022. "The Feller Coupling for random derangements," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 1139-1164.

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