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arXiv · 1811.03183

Fox H-kernel and $\theta$-deformation of the Cauchy two-matrix model and Bures ensemble

Peter J Forrester·Shi-Hao Li
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Abstract

A $\theta$-deformation of the Laguerre weighted Cauchy two-matrix model, and the Bures ensemble, is introduced. Such a deformation is familiar from the Muttalib-Borodin ensemble. The $\theta$-deformed Cauchy-Laguerre two-matrix model is a two-component determinantal point process. It is shown that the correlation kernel, and its hard edge scaled limit, can be written as the Fox H-functions, generalising the Meijer G-function class known from the study of the case $\theta= 1$. In the $\theta=1$ case, it is shown Laguerre-Bures ensemble is related to the Laguerre-Cauchy two-matrix model, notwithstanding the Bures ensemble corresponds to a Pfaffian point process. This carries over to the $\theta$-deformed case, allowing explicit expressions involving Fox H-functions for the correlation kernel, and its hard edge scaling limit, to be obtained.

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Peter J Forrester, Shi-Hao Li. 2018-11-07. Fox H-kernel and $\theta$-deformation of the Cauchy two-matrix model and Bures ensemble. https://arxiv.org/abs/1811.03183

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