Random anti-commuting Hermitian matrices

John E. McCarthy, Hazel T. McCarthy

Research output: Contribution to journalArticlepeer-review

Abstract

We consider pairs of anti-commuting 2p-by-2p Hermitian matrices that are chosen randomly with respect to a Gaussian measure. Generically such a pair decomposes into the direct sum of 2-by-2 blocks on which the first matrix has eigenvalues }xj and the second has eigenvalues }yj. We call {(xj, yj )} the skew spectrum of the pair. We derive a formula for the probability density of the skew spectrum, and show that the elements are repelling..

Original languageEnglish
Article number2450019
JournalRandom Matrices: Theory and Application
Volume13
Issue number4
DOIs
StatePublished - Oct 1 2024

Keywords

  • Random matrix tuples
  • anti-commuting matrices

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