Hard edge limit of the product of two strongly coupled random matrices

Akemann G, Strahov E (2016)
Nonlinearity 29(12): 3743.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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Abstract / Bemerkung
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.
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Zeitschriftentitel
Nonlinearity
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29
Zeitschriftennummer
12
Artikelnummer
3743
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Akemann G, Strahov E. Hard edge limit of the product of two strongly coupled random matrices. Nonlinearity. 2016;29(12): 3743.
Akemann, G., & Strahov, E. (2016). Hard edge limit of the product of two strongly coupled random matrices. Nonlinearity, 29(12), 3743. doi:10.1088/0951-7715/29/12/3743
Akemann, G., and Strahov, E. (2016). Hard edge limit of the product of two strongly coupled random matrices. Nonlinearity 29:3743.
Akemann, G., & Strahov, E., 2016. Hard edge limit of the product of two strongly coupled random matrices. Nonlinearity, 29(12): 3743.
G. Akemann and E. Strahov, “Hard edge limit of the product of two strongly coupled random matrices”, Nonlinearity, vol. 29, 2016, : 3743.
Akemann, G., Strahov, E.: Hard edge limit of the product of two strongly coupled random matrices. Nonlinearity. 29, : 3743 (2016).
Akemann, Gernot, and Strahov, Eugene. “Hard edge limit of the product of two strongly coupled random matrices”. Nonlinearity 29.12 (2016): 3743.

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