## Abstract

The singular values of a product of M independent Ginibre matrices of size N×N form a determinantal point process. Near the soft edge, as both M and N go to infinity in such a way that M/N→α, α>0, a scaling limit emerges. We consider a gap probability for the corresponding limiting determinantal process, namely, the probability that there are no particles in the interval (a,+∞). We derive a Tracy–Widom-like formula in terms of the unique solution of a certain matrix Riemann–Hilbert problem of size 2 × 2. The right-tail asymptotics for this solution is obtained by the Deift–Zhou non-linear steepest descent analysis.

Original language | American English |
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Article number | 105687 |

Journal | Journal of Approximation Theory |

Volume | 274 |

DOIs | |

State | Published - Feb 2022 |

## Keywords

- Determinantal point processes
- Gap probabilities
- Products of random matrices
- Riemann–Hilbert problems
- Singular value statistics

## All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics
- Numerical Analysis
- General Mathematics