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Rank one HCIZ at high temperature: interpolating between classical and free convolutions
by Pierre Mergny, Marc Potters
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Submission summary
Authors (as Contributors): | Pierre Mergny |
Submission information | |
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Preprint link: | scipost_202108_00047v1 |
Date accepted: | 2021-11-18 |
Date submitted: | 2021-08-18 12:03 |
Submitted by: | Mergny, Pierre |
Submitted to: | SciPost Physics |
Ontological classification | |
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Academic field: | Physics |
Specialties: |
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Approach: | Theoretical |
Abstract
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.
Published as SciPost Phys. 12, 022 (2022)
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Anonymous Report 1 on 2021-10-27 (Invited Report)
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The paper looks now OK to me and may be published in that form.