Limiting Spectral Distribution of Sum of Unitary and Orthogonal Matrices

2012/08/25 by Anirban Basak, Basak, Anirban, Amir Dembo +1
Mathematics · #46L53 #60B10 #60B20 #FOS: Mathematics #Graph theory and applications #Probability (math.PR) #Random Matrices and Applications #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1208.5100

openalex publication_date 2012/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the empirical eigenvalue measure for sum of d independent Haar distributed n-dimensional unitary matrices, converge for n → ∞ to the Brown measure of the free sum of d Haar unitary operators. The same applies for independent Haar distributed n-dimensional orthogonal matrices. As a byproduct of our approach, we relax the requirement of uniformly bounded imaginary part of Stieltjes transform of T_n that is made in [Guionnet, Krishnapur, Zeitouni; Theorem 1].

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