Asymptotic mean density of sub-unitary ensemble

Abstract

The large N limit of mean spectral density for the ensemble of NxN sub-unitary matrices derived by Wei and Fyodorov (J. Phys. A: Math. Theor. 41 (2008) 50201) is calculated by a modification of the saddle point method. It is shown that the result coincides with the one obtained within the free probability theory by Haagerup and Larsen (J. Funct. Anal. 176 (2000) 331).

References in corpus (3)

• Truncations of random unitary matrices
• On the resonance eigenstates of an open quantum baker map
• On the mean density of complex eigenvalues for an ensemble of random matrices with prescribed singular values

Cited by in corpus (6)

• Eigenvalue spectra of asymmetric random matrices for multi-component neural networks
• One-component plasma on a spherical annulus and a random matrix ensemble
• Commutative law for products of infinitely large isotropic random matrices
• Local random vector model for semiclassical fractal structure of chaotic resonance states
• Resonance states of the three-disk scattering system
• Spectral Properties of Non-Unitary Band Matrices