2012/08/25 by Anirban Basak, Basak, Anirban, Amir Dembo +1 · 1 citation
Mathematics · #46L53 #60B10 #60B20 #Bounded function #Circular ensemble #Circular law #Combinatorics #Computer science #Discrete mathematics #Distribution (mathematics) #Eigenvalues and eigenvectors #FOS: Mathematics #Graph theory and applications #Haar #Haar measure #Limiting #Mathematical analysis #Mathematics #Measure (data warehouse) #Orthogonal basis #Orthogonal matrix #Physics #Probability (math.PR) #Pure mathematics #Quantum mechanics #Random Matrices and Applications #Random variable #Spectral Theory in Mathematical Physics #Statistics #Unitary group #Unitary matrix #Unitary state #math.PR #msc:46L53 #msc:60B10 #msc:60B20
paper · pdf · doi:10.48550/arxiv.1208.5100
published in arXiv (Cornell University) (Cornell University) · 17 pages; changes in the presentation style, several minor changes in proofs
openalex publication_date 2012/08/25 · arxiv created 2013/07/04 · arxiv updated 2013/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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 Tn that is made in [Guionnet, Krishnapur, Zeitouni; Theorem 1].