@inbook{5ddf302609cd48be9d85c7f1cfa29b9a,

title = "Asymptotic Behaviour of Poisson-Dirichlet Distribution and Random Energy Model",

abstract = "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{\textquoteright}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.",

keywords = "Dirichlet process, Large deviations, Phase transition, Poisson-Dirichlet distribution, Random energy model",

author = "Shui Feng and Youzhou Zhou",

note = "Publisher Copyright: {\textcopyright} 2015, Springer International Publishing Switzerland.",

year = "2015",

doi = "10.1007/978-3-319-13984-5_7",

language = "English",

series = "Progress in Probability",

publisher = "Birkhauser",

pages = "141--155",

booktitle = "Progress in Probability",

}