TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.12.1.022
TI  - Rank one HCIZ at high temperature: interpolating between classical and free convolutions
PY  - 2022/01/14
UR  - https://www.scipost.org/SciPostPhys.12.1.022
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 12
IS  - 1
SP  - 022
A1  - Mergny, Pierre
AU  - Potters, Marc
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.12.1.022,
	title={{Rank one HCIZ at high temperature: interpolating between classical and free convolutions}},
	author={Pierre Mergny and Marc Potters},
	journal={SciPost Phys.},
	volume={12},
	pages={022},
	year={2022},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.12.1.022},
	url={https://scipost.org/10.21468/SciPostPhys.12.1.022},
}