2015/01/08 by Gene S. Kopp, Steven J. Miller, Kopp, Gene S. +1 · 1 citation
Chemistry · Mathematics · Physics and Astronomy · #15B52 (primary) #60F05 (secondary) #Advanced Algebra and Geometry #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Molecular spectroscopy and chirality #Probability (math.PR) #Random Matrices and Applications #math-ph #math.MP #math.PR #msc:15B52 #msc:60F05
paper · pdf · doi:10.48550/arxiv.1501.01848
Version 2.0, 15 pages, 3 figures; updated with additional references to the literature (the problem had been considered by others earlier, under the name fixed trace ensembles
openalex publication_date 2015/01/08 · arxiv created 2015/02/02 · arxiv updated 2015/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The spherical orthogonal, unitary, and symplectic ensembles (SOE/SUE/SSE) Sβ(N,r) consist of N × N real symmetric, complex hermitian, and quaternionic self-adjoint matrices of Frobenius norm r, made into a probability space with the uniform measure on the sphere. For each of these ensembles, we determine the joint eigenvalue distribution for each N, and we prove the empirical spectral measures rapidly converge to the semicircular distribution as N → ∞. In the unitary case (β=2), we also find an explicit formula for the empirical spectral density for each N.