General Tridiagonal Random Matrix Models, Limiting Distributions and Fluctuations

Details General Tridiagonal Random Matrix Models, Limiting Distributions and Fluctuations General Tridiagonal Random Matrix Models, Limiting Distributions and Fluctuations

2006-10-27

arxiv.org/abs/math/0610827v3

Mathematics

Probability

Several mistakes and errors are now corrected. This version will appear in Probability Theory and Related Fields

Scientific paper

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.

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