--- res: bibo_abstract: - 'We compare finite rank perturbations of the following three ensembles of complex rectangular random matrices: First, a generalised Wishart ensemble with one random and two fixed correlation matrices introduced by Borodin and Péché, second, the product of two independent random matrices where one has correlated entries, and third, the case when the two random matrices become also coupled through a fixed matrix. The singular value statistics of all three ensembles is shown to be determinantal and we derive double contour integral representations for their respective kernels. Three different kernels are found in the limit of infinite matrix dimension at the origin of the spectrum. They depend on finite rank perturbations of the correlation and coupling matrices and are shown to be integrable. The first kernel (I) is found for two independent matrices from the second, and two weakly coupled matrices from the third ensemble. It generalises the Meijer G-kernel for two independent and uncorrelated matrices. The third kernel (III) is obtained for the generalised Wishart ensemble and for two strongly coupled matrices. It further generalises the perturbed Bessel kernel of Desrosiers and Forrester. Finally, kernel (II), found for the ensemble of two coupled matrices, provides an interpolation between the kernels (I) and (III), generalising previous findings of part of the authors.@eng' bibo_authorlist: - foaf_Person: foaf_givenName: Gernot foaf_name: Akemann, Gernot foaf_surname: Akemann - foaf_Person: foaf_givenName: Tomasz foaf_name: Checinski, Tomasz foaf_surname: Checinski - foaf_Person: foaf_givenName: Dangzheng foaf_name: Liu, Dangzheng foaf_surname: Liu foaf_workInfoHomepage: http://www.librecat.org/personId=2F947E34-F248-11E8-B48F-1D18A9856A87 - foaf_Person: foaf_givenName: Eugene foaf_name: Strahov, Eugene foaf_surname: Strahov bibo_doi: 10.1214/18-aihp888 bibo_issue: '1' bibo_volume: 55 dct_date: 2019^xs_gYear dct_identifier: - UT:000456070200013 dct_isPartOf: - http://id.crossref.org/issn/0246-0203 dct_language: eng dct_publisher: Institute of Mathematical Statistics@ dct_title: 'Finite rank perturbations in products of coupled random matrices: From one correlated to two Wishart ensembles@' ...