--- _id: '7423' abstract: - lang: eng text: '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.' article_processing_charge: No article_type: original author: - first_name: Gernot full_name: Akemann, Gernot last_name: Akemann - first_name: Tomasz full_name: Checinski, Tomasz last_name: Checinski - first_name: Dangzheng full_name: Liu, Dangzheng id: 2F947E34-F248-11E8-B48F-1D18A9856A87 last_name: Liu - first_name: Eugene full_name: Strahov, Eugene last_name: Strahov citation: ama: 'Akemann G, Checinski T, Liu D, Strahov E. Finite rank perturbations in products of coupled random matrices: From one correlated to two Wishart ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques. 2019;55(1):441-479. doi:10.1214/18-aihp888' apa: 'Akemann, G., Checinski, T., Liu, D., & Strahov, E. (2019). Finite rank perturbations in products of coupled random matrices: From one correlated to two Wishart ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques. Institute of Mathematical Statistics. https://doi.org/10.1214/18-aihp888' chicago: 'Akemann, Gernot, Tomasz Checinski, Dangzheng Liu, and Eugene Strahov. “Finite Rank Perturbations in Products of Coupled Random Matrices: From One Correlated to Two Wishart Ensembles.” Annales de l’Institut Henri Poincaré, Probabilités et Statistiques. Institute of Mathematical Statistics, 2019. https://doi.org/10.1214/18-aihp888.' ieee: 'G. Akemann, T. Checinski, D. Liu, and E. Strahov, “Finite rank perturbations in products of coupled random matrices: From one correlated to two Wishart ensembles,” Annales de l’Institut Henri Poincaré, Probabilités et Statistiques, vol. 55, no. 1. Institute of Mathematical Statistics, pp. 441–479, 2019.' ista: 'Akemann G, Checinski T, Liu D, Strahov E. 2019. Finite rank perturbations in products of coupled random matrices: From one correlated to two Wishart ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques. 55(1), 441–479.' mla: 'Akemann, Gernot, et al. “Finite Rank Perturbations in Products of Coupled Random Matrices: From One Correlated to Two Wishart Ensembles.” Annales de l’Institut Henri Poincaré, Probabilités et Statistiques, vol. 55, no. 1, Institute of Mathematical Statistics, 2019, pp. 441–79, doi:10.1214/18-aihp888.' short: G. Akemann, T. Checinski, D. Liu, E. Strahov, Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55 (2019) 441–479. date_created: 2020-01-30T10:36:50Z date_published: 2019-02-01T00:00:00Z date_updated: 2023-09-06T14:58:39Z day: '01' department: - _id: LaEr doi: 10.1214/18-aihp888 external_id: arxiv: - '1704.05224' isi: - '000456070200013' intvolume: ' 55' isi: 1 issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1704.05224 month: '02' oa: 1 oa_version: Preprint page: 441-479 publication: Annales de l'Institut Henri Poincaré, Probabilités et Statistiques publication_identifier: issn: - 0246-0203 publication_status: published publisher: Institute of Mathematical Statistics quality_controlled: '1' status: public title: 'Finite rank perturbations in products of coupled random matrices: From one correlated to two Wishart ensembles' type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 55 year: '2019' ...