DISTRIBUTION OF EIGENVALUES FOR SOME SETS OF RANDOM MATRICES

1967/04/30 by V A Marčenko, L. А. Pastur, L A Pastur · 33 citations
Mathematics · #Advanced Algebra and Geometry #Combinatorics #Distribution (mathematics) #Eigenvalues and eigenvectors #Mathematical analysis #Mathematics #Physics #Random Matrices and Applications #Random matrix #Spectral Theory in Mathematical Physics

paper · doi:10.1070/sm1967v001n04abeh001994

crossref issued 1967/04/30 · crossref published 1967/04/30 · crossref published-print 1967/04/30 · openalex publication_date 1967/04/30 · crossref created 2005/11/09 · crossref published-online 2007/10/18 · crossref deposited 2024/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05 · crossref indexed 2026/08/05

Abstract

In this paper we study the distribution of eigenvalues for two sets of random Hermitian matrices and one set of random unitary matrices. The statement of the problem as well as its method of investigation go back originally to the work of Dyson [i] and I. M. Lifsic [2], [3] on the energy spectra of disordered systems, although in their probability character our sets are more similar to sets studied by Wigner [4]. Since the approaches to the sets we consider are the same, we present in detail only the most typical case. The corresponding results for the other two cases are presented without proof in the last section of the paper. §1. Statement of the problem and survey of results We shall consider as acting in iV-dimensiona l unitary space ///v, a selfadjoint operator BN (re) of the form

Citations

• On the Distribution of the Roots of Certain Symmetric Matrices

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