Tridiagonal random matrices, an analytic approach

2025/12/03 by Lucas Babet, Ionel Popescu, Babet, Lucas +1 · 1 citation
Computer Science · Mathematics · #Markov Chains and Monte Carlo Methods #Quantum Information and Cryptography #Random Matrices and Applications #math.OA #math.PR #math.SP

paper · pdf · doi:10.48550/arxiv.2512.03628

openalex publication_date 2025/12/03 · openalex created_date 2025/12/05 · openalex updated_date 2026/08/01

Abstract

In this paper, we study the limiting distribution of the eigenvalues for random tridiagonal matrix models. In the paper \citeP09, the limiting distribution is well described by its moments. Here, an analytical approach allows us, as in the case of Wigner matrices, to relax the assumptions on the random variables. With this method, we proved the convergence of the spectral distribution under an assumption on the second moment. We discuss also about an algebraic approach for the tridiagonal models, which are more complicated than the classic freeness.

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Cited by

• Enumeration of maps with the Dumitriu-Edelman model

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