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Asymptotic Properties of Random Restricted Partitions

Author

Listed:
  • Tiefeng Jiang

    (School of Statistics, University of Minnesota, 224 Church Street S. E., Minneapolis, MN 55455, USA
    These authors contributed equally to this work.)

  • Ke Wang

    (Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong
    These authors contributed equally to this work.)

Abstract

We study two types of probability measures on the set of integer partitions of n with at most m parts. The first one chooses the partition with a chance related to its largest part only. We obtain the limiting distributions of all of the parts together and that of the largest part as n tending to infinity for m fixed or tending to infinity with m = o ( n 1 / 3 ) . In particular, if m goes to infinity not too fast, the largest part satisfies the central limit theorem. The second measure is very general and includes the Dirichlet and uniform distributions as special cases. The joint asymptotic distributions of the parts are derived by taking limits of n and m in the same manner as that in the first probability measure.

Suggested Citation

  • Tiefeng Jiang & Ke Wang, 2023. "Asymptotic Properties of Random Restricted Partitions," Mathematics, MDPI, vol. 11(2), pages 1-30, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:417-:d:1034161
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