Large deviation for the empirical eigenvalue density of truncated Haar unitary matrices

D. Petz, Júlia Réffy

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

Let U m be an m×m Haar unitary matrix and U [ m,n ] be its n×n truncation. In this paper the large deviation is proven for the empirical eigenvalue density of U [ m,n ] as m/n→λ and n→∞. The rate function and the limit distribution are given explicitly. U [ m,n ] is the random matrix model of quq, where u is a Haar unitary in a finite von Neumann algebra, q is a certain projection and they are free. The limit distribution coincides with the Brown measure of the operator quq.

Original languageEnglish
Pages (from-to)175-189
Number of pages15
JournalProbability Theory and Related Fields
Volume133
Issue number2
DOIs
Publication statusPublished - Oct 2005

Fingerprint

Unitary matrix
Limit Distribution
Large Deviations
Finite Von Neumann Algebras
Eigenvalue
Rate Function
Matrix Models
Random Matrices
Truncation
Projection
Operator
Large deviations
Limit distribution
Eigenvalues

Keywords

  • Free probability
  • Haar unitary
  • Joint eigenvalue distribution
  • Large deviation
  • Random matrices
  • Random matrix model
  • Rate function
  • Truncated Haar unitary

ASJC Scopus subject areas

  • Mathematics(all)
  • Analysis
  • Statistics and Probability

Cite this

Large deviation for the empirical eigenvalue density of truncated Haar unitary matrices. / Petz, D.; Réffy, Júlia.

In: Probability Theory and Related Fields, Vol. 133, No. 2, 10.2005, p. 175-189.

Research output: Contribution to journalArticle

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