2018/11/07 by Peter J. Forrester, Peter J Forrester, Forrester, Peter J +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Physical sciences #Mathematical Physics (math-ph) #Random Matrices and Applications #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1811.03183
24 pages
arxiv created 2018/11/07 · openalex publication_date 2018/11/07 · arxiv updated 2018/11/09 · openalex created_date 2018/11/16 · openalex updated_date 2026/07/28
A θ-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 θ-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 θ= 1. In the θ=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 θ-deformed case, allowing explicit expressions involving Fox H-functions for the correlation kernel, and its hard edge scaling limit, to be obtained.