Edge scaling limit of the spectral radius for random normal matrix ensembles at hard edge

Abstract

We investigate a random normal matrix model with eigenvalues forced to be in the droplet, the support of the equilibrium measure associated with an external field. For radially symmetric external fields, 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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Cited by in corpus (7)

• A localization theorem for the planar Coulomb gas in an external field
• On boundary confinements for the Coulomb gas
• Wronskian structures of planar symplectic ensembles
• Edge fluctuations for random normal matrix ensembles
• Functional Central Limit Theorems for Constrained Mittag-Leffler Ensemble in Hard Edge Scaling
• Edge behavior of two-dimensional Coulomb gases near a hard wall
• Aspects of Coulomb gases