Asymptotic Behaviour of Poisson-Dirichlet Distribution and Random Energy Model

Shui Feng*, Youzhou Zhou

*Corresponding author for this work

Research output: Chapter in Book or Report/Conference proceedingChapterpeer-review

2 Citations (Scopus)


The family of Poisson-Dirichlet distributions is a collection of two-parameter probability distributions { PD(α, θ): 0 ≤ α< 1, α+ θ> 0 } defined on the infinite-dimensional simplex. The parameters α and θ correspond to the stable and gamma component respectively. The distribution PD(α, 0) arises in the thermodynamic limit of the Gibbs measure of Derrida’s Random Energy Model (REM) in the low temperature regime. In this setting α can be written as the ratio between the temperature T and a critical temperature Tc. In this paper, we study the asymptotic behaviour of PD(α, θ) as α converges to one or equivalently when the temperature approaches the critical value Tc.

Original languageEnglish
Title of host publicationProgress in Probability
Number of pages15
Publication statusPublished - 2015
Externally publishedYes

Publication series

NameProgress in Probability
ISSN (Print)1050-6977
ISSN (Electronic)2297-0428


  • Dirichlet process
  • Large deviations
  • Phase transition
  • Poisson-Dirichlet distribution
  • Random energy model

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