Hard edge limit of the product of two strongly coupled random matrices. (20th October 2016)

• Record Type: Journal Article
• Authors: Akemann, Gernot; Strahov, Eugene
• Is Part Of: Nonlinearity. Volume 29:Number 12(2016:Dec.)
• Page Start: 3743
• Page End: 3776
• Publication Date: 2016-10-20
• Subjects: products of complex random matrices -- determinantal point processes -- Meijer G-kernel -- Bessel-kernel -- interpolating ensembles; 15B 52 -- 33E20 -- 60G55; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/0951-7715/29/12/3743
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: We investigate the hard edge scaling limit of the ensemble defined by the squared singular values of the product of two coupled complex random matrices. When taking the coupling parameter to be dependent on the size of the product matrix, in a certain double scaling regime at the origin the two matrices become strongly coupled and we obtain a new hard edge limiting kernel. It interpolates between the classical Bessel-kernel describing the hard edge scaling limit of the Laguerre ensemble of a single matrix, and the Meijer G-kernel of Kuijlaars and Zhang describing the hard edge scaling limit for the product of two independent Gaussian complex matrices. It differs from the interpolating kernel of Borodin to which we compare as well.