Rank one HCIZ at high temperature: interpolating between classical and free convolutions

We study the rank one Harish-Chandra-Itzykson-Zuber integral in the limit where \(\frac{N \beta}{2} \to c \), called the high temperature regime and show that it can be used to construct a promising one-parameter interpolation, with parameter \(c\) between the classical and the free convolution. Thi...

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Vydané v:arXiv.org
Hlavní autori: Mergny, Pierre, Potters, Marc
Médium: Paper
Jazyk:English
Vydavateľské údaje: Ithaca Cornell University Library, arXiv.org 22.01.2021
Predmet:
Convolution
High temperature
Interpolation
Parameters
Theorems
ISSN:2331-8422
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Popis
Shrnutí:We study the rank one Harish-Chandra-Itzykson-Zuber integral in the limit where \(\frac{N \beta}{2} \to c \), called the high temperature regime and show that it can be used to construct a promising one-parameter interpolation, with parameter \(c\) between the classical and the free convolution. This \(c\)-convolution has a simple interpretation in terms of another associated family of distribution indexed by \(c\), called the Markov-Krein transform: the \(c\)-convolution of two distributions corresponds to the classical convolution of their Markov-Krein transforms. We derive first cumulants-moments relations, a central limit theorem, a Poisson limit theorem and shows several numerical examples of \(c\)-convoluted distributions.
Bibliografia:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
content type line 50
ISSN:2331-8422
DOI:10.48550/arxiv.2101.01810