## Abstract

Consider the product of m independent n×n random matrices from the spherical ensemble for m≥1. The spectral radius is defined as the maximum absolute value of the n eigenvalues of the product matrix. When m=1, the limiting distribution for the spectral radii has been obtained by Jiang and Qi (2017). In this paper, we investigate the limiting distributions for the spectral radii in general. When m is a fixed integer, we show that the spectral radii converge weakly to distributions of functions of independent Gamma random variables. When m=m_{n} tends to infinity as n goes to infinity, we show that the logarithmic spectral radii have a normal limit.

Original language | English (US) |
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Pages (from-to) | 1165-1176 |

Number of pages | 12 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 461 |

Issue number | 2 |

DOIs | |

State | Published - May 15 2018 |

### Bibliographical note

Publisher Copyright:© 2018 Elsevier Inc.

## Keywords

- Limiting distribution
- Product ensemble
- Random matrix
- Spectral radius
- Spherical ensemble