2006/10/26 by Peter Eichelsbacher, Eichelsbacher, Peter, Michael Stolz +1
Mathematics · #60F10 #Advanced Algebra and Geometry #Advanced Operator Algebra Research #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.math/0610811
openalex publication_date 2006/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In his seminal 1962 paper on the ``threefold way'', Freeman Dyson classified the spaces of matrices that support the random matrix ensembles deemed relevant from the point of view of classical quantum mechanics. Recently, Heinzner, Huckleberry and Zirnbauer have obtained a similar classification based on less restrictive assumptions, thus taking care of the needs of modern mesoscopic physics. Their list is in one-to-one correspondence with the infinite families of Riemannian symmetric spaces as classified by Cartan. The present paper develops the corresponding random matrix theories, with a special emphasis on large deviation principles.