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TITLE Edge Scaling Limit of the Spectral Radius for Random Normal Matrix Ensembles at Hard Edge
KIAS AUTHORS Seo, Seong-Mi
JOURNAL JOURNAL OF STATISTICAL PHYSICS, 2020
ARCHIVE arXiv:1508.06591v2
ABSTRACT We investigate local statistics of eigenvalues for random normal matrices, represented as 2D determinantal Coulomb gases, in the casewhen the eigenvalues are forced to be in the support of the equilibrium measure associated with an external field. For radially symmetric external fields with sufficient growth at infinity, we show that the fluctuations of the spectral radius around a hard edge tend to follow an exponential distribution as the number of eigenvalues tends to infinity. As a corollary, we obtain the order statistics of the moduli of eigenvalues.
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