## 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.

Original language | American English |
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Pages (from-to) | 3743-3776 |

Number of pages | 34 |

Journal | Nonlinearity |

Volume | 29 |

Issue number | 12 |

DOIs | |

State | Published - 20 Oct 2016 |

### Bibliographical note

Publisher Copyright:© 2016 IOP Publishing Ltd & London Mathematical Society.

## Keywords

- Bessel-kernel
- Meijer G-kernel
- determinantal point processes
- interpolating ensembles
- products of complex random matrices