Title

Power-law eigenvalue density, scaling, and critical random-matrix ensembles

Authors

Authors

K. A. Muttalib;M. E. H. Ismail

Comments

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Abbreviated Journal Title

Phys. Rev. E

Keywords

SPECTRAL STATISTICS; LEVY MATRICES; TRANSITION; MODELS; Physics, Fluids & Plasmas; Physics, Mathematical

Abstract

We consider a class of rotationally invariant unitary random matrix ensembles where the eigenvalue density falls off as an inverse power law. Under a scaling appropriate for such power-law densities (different from the scaling required in Gaussian random matrix ensembles), we calculate exactly the two-level kernel that determines all eigenvalue correlations. We show that such ensembles belong to the class of critical ensembles.

Journal Title

Physical Review E

Volume

76

Issue/Number

5

Publication Date

1-1-2007

Document Type

Article

Language

English

First Page

5

WOS Identifier

WOS:000251326100012

ISSN

1539-3755

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