General Tridiagonal Random Matrix Models, Limiting Distributions and Fluctuations
概率论
2008-02-18 v3 算子代数
摘要
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.
引用
@article{arxiv.math/0610827,
title = {General Tridiagonal Random Matrix Models, Limiting Distributions and Fluctuations},
author = {Ionel Popescu},
journal= {arXiv preprint arXiv:math/0610827},
year = {2008}
}
备注
Several mistakes and errors are now corrected. This version will appear in Probability Theory and Related Fields