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Power law eigenvalue density, scaling and critical random matrix ensembles

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 نشر من قبل K. A. Muttalib
 تاريخ النشر 2007
  مجال البحث فيزياء
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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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