How fast does spectral radius of truncated circular unitary ensemble converge?

2025/06/20 by Ma, Yutao, Meng, Xujia · 2 citations
Computer Science · Mathematics · #15B52 #60F10 #Circular ensemble #Constant (computer programming) #Eigenvalues and eigenvectors #FOS: Mathematics #Mathematical Inequalities and Applications #Matrix Theory and Algorithms #Probability (math.PR) #RADIUS #Random Matrices and Applications #Spectrum (functional analysis) #Unitary state

paper · pdf · doi:10.48550/arxiv.2506.16967

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2025/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Let z₁, ⋯, z_p be the eigenvalues of A, which is the left-top p× p submatrix of an n× n Haar-invariant unitary matrix. Suppose there exist two constants 0

Citations

• Convergence rate of extreme eigenvalue of Ginibre ensembles to Gumbel distribution
• Optimal W₁ and Berry-Esseen bound between the spectral radius of large Chiral non-Hermitian random matrices and Gumbel
• Exact convergence rate of spectral radius of complex Ginibre to Gumbel distribution
• Universality of extremal eigenvalues of large random matrices
• On the rightmost eigenvalue of non-Hermitian random matrices
• Spectral Radii of Large Non-Hermitian Random Matrices
• Extremal laws for the real Ginibre ensemble
• From Gumbel to Tracy-Widom

Cited by

• From Gaussian to Gumbel: extreme eigenvalues of complex Ginibre products with exact rates
• Revisit on the convergence rate of normal extremes

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• Limiting spectral distribution of the product of truncated Haar unitary matrices
• Limiting Spectral Distribution of Sum of Unitary and Orthogonal Matrices
• Precise asymptotics for the spectral radius of a large random matrix