Power law eigenvalue density, scaling and critical random matrix ensembles

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

doi:10.1103/physreve.76.051105

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arXiv · 0710.4527

Power law eigenvalue density, scaling and critical random matrix ensembles

K. A. Muttalib·Mourad E. H. Ismail

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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 new 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.

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K. A. Muttalib, Mourad E. H. Ismail. 2007-10-24. Power law eigenvalue density, scaling and critical random matrix ensembles. https://doi.org/10.1103/physreve.76.051105

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