General Tridiagonal Random Matrix Models, Limiting Distributions and Fluctuations

2006/10/27 by Ionel Popescu, Popescu, Ionel · 2 citations
Mathematics · #Random Matrices and Applications #Stochastic processes and statistical mechanics #Advanced Combinatorial Mathematics

paper · pdf · doi:10.48550/arxiv.math/0610827

Abstract

In this paper we discuss general tridiagonal matrix models which are natural extensions of the ones given by Dumitriu and Edelman. We prove here the convergence of the distribution of the eigenvalues and compute the limiting distributions in some particular cases. We also discuss the limit of fluctuations, which, in a general context, turn out to be Gaussian. For the case of several random matrices, we prove the convergence of the joint moments and the convergence of the fluctuations to a Gaussian family.

Citations

• Limit laws for Random matrices and free products
• On the Distribution of the Roots of Certain Symmetric Matrices

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