On the Matrix Range of Random Matrices

Malte Gerhold, Orr Moshe Shalit

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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 languageEnglish
Pages (from-to)527-545
Number of pages19
JournalJournal of Operator Theory
Issue number2
StatePublished - 1 Mar 2021
Externally publishedYes


  • Matrix range
  • matrix convexity
  • random matrices

ASJC Scopus subject areas

  • Algebra and Number Theory


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