Tridiagonal random matrices, an analytic approach
Probability
2025-12-04 v1 Operator Algebras
Spectral Theory
Abstract
In this paper, we study the limiting distribution of the eigenvalues for random tridiagonal matrix models. 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.
Cite
@article{arxiv.2512.03628,
title = {Tridiagonal random matrices, an analytic approach},
author = {Lucas Babet and Ionel Popescu},
journal= {arXiv preprint arXiv:2512.03628},
year = {2025}
}