Eigenvalue density of the wishart matrix and large deviations

Fumio Hiai, Dénes Petz

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

A large deviation theorem is obtained for a certain sequence of random measures which includes the empirical eigenvalue distribution of Wishart matrices, as the matrix size tends to infinity. The rate function is convex and one of its ingredients is the logarithmic energy. In the case of the singular Wishart matrix, the limit distribution has an atom.

Original languageEnglish
Pages (from-to)633-646
Number of pages14
JournalInfinite Dimensional Analysis, Quantum Probability and Related Topics
Volume1
Issue number4
Publication statusPublished - Oct 1998

Fingerprint

Wishart Matrix
Large Deviations
eigenvalues
Eigenvalue
deviation
Eigenvalue Distribution
Singular matrix
Random Measure
Rate Function
Empirical Distribution
Limit Distribution
matrices
Logarithmic
Infinity
Tend
ingredients
infinity
theorems
Energy
Theorem

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Mathematical Physics
  • Statistics and Probability
  • Statistical and Nonlinear Physics

Cite this

Eigenvalue density of the wishart matrix and large deviations. / Hiai, Fumio; Petz, Dénes.

In: Infinite Dimensional Analysis, Quantum Probability and Related Topics, Vol. 1, No. 4, 10.1998, p. 633-646.

Research output: Contribution to journalArticle

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