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Finite rank perturbations in products of coupled random matrices: From one correlated to two Wishart
2018-04-23 00:00:00

报告题目:

Finite rank perturbations in products of coupled random matrices: From one correlated to two Wishart ensembles

报 告 人:

刘党政 教授(中国科学技术大学)

报告时间:

2018年04月27日 15:00--16:00

报告地点:

理学院东北楼二楼报告厅(209)

报告摘要:

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 Peche, 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, which depend on finite rank perturbations of the correlation and coupling matrices. This is based on joint work with G. Akemann, T. Checinski and E. Strahov