## Abstract

This note treats a simple minded question: what does a typical random matrix range look like? We study the relationship between various modes of convergence for tuples of operators on the one hand, and continuity of matrix ranges with respect to the Hausdorff metric on the other. In particular, we show that the matrix range of a tuple generating a continuous field of C*- algebras is continuous in the sense that every level is continuous in the Hausdorff metric. Using this observation together with known results on strong convergence in distribution of matrix ensembles, we identify the limit matrix ranges to which the matrix ranges of independent Wigner or Haar ensembles converge.

Original language | English |
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Pages (from-to) | 527-545 |

Number of pages | 19 |

Journal | Journal of Operator Theory |

Volume | 85 |

Issue number | 2 |

DOIs | |

State | Published - 1 Mar 2021 |

Externally published | Yes |

## Keywords

- Matrix range
- matrix convexity
- random matrices

## ASJC Scopus subject areas

- Algebra and Number Theory