A large deviation theorem for the empirical eigenvalue distribution of random unitary matrices

Fumio Hiai, D. Petz

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

It is shown that the empirical eigenvalue distribution of suitably distributed random unitary matrices satisfies the large deviation principle as the matrix size goes to infinity. The primary term of the rate function is the logarithmic energy (or the minus sign of Voiculescu's free entropy). Examples of random unitaries are also discussed, one of them is related to the work of Gross and Witten in quantum physics.

Original languageEnglish
Pages (from-to)71-85
Number of pages15
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Volume36
Issue number1
Publication statusPublished - Jan 2000

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Free Entropy
Eigenvalue Distribution
Quantum Physics
Unitary matrix
Large Deviation Principle
Rate Function
Empirical Distribution
Random Matrices
Gross
Large Deviations
Logarithmic
Infinity
Term
Energy
Theorem
Large deviations
Eigenvalues
Entropy
Physics

Keywords

  • Eigenvalue density
  • Large deviation
  • Logarithmic energy
  • Random unitary matrix

ASJC Scopus subject areas

  • Statistics and Probability

Cite this

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