Fox H-kernel and θ-deformation of the Cauchy Two-Matrix Model and Bures Ensemble

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 in terms of particular 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 that the Laguerre-Bures ensemble is related to the Laguerre-Cauchy two-matrix model, notwithstanding the Bures ensemble correspondi..