Spectral distributions and isospectral sets of tridiagonal matrices

2002/07/03 by Peter Gibson, Peter C. Gibson, Gibson, Peter
Mathematics · #FOS: Mathematics #Mathematical functions and polynomials #Point processes and geometric inequalities #Random Matrices and Applications #Spectral Theory (math.SP) #math.SP

paper · pdf · doi:10.48550/arxiv.math/0207041

arxiv created 2002/07/03 · openalex publication_date 2002/07/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We analyze the correspondence between finite sequences of finitely supported probability distributions and finite-dimensional, real, symmetric, tridiagonal matrices. In particular, we give an intrinsic description of the topology induced on sequences of distributions by the usual Euclidean structure on matrices. Our results provide an analytical tool with which to study ensembles of tridiagonal matrices, important in certain inverse problems and integrable systems. As an application, we prove that the Euler characteristic of any generic isospectral set of symmetric, tridiagonal matrices is a tangent number.

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