General tridiagonal random matrix models, limiting distributions and fluctuations
成果类型：
Article
署名作者：
Popescu, Ionel
署名单位：
University System of Georgia; Georgia Institute of Technology; Institute of Mathematics of the Romanian Academy
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-008-0145-y
发表日期：
2009
页码：
179-220
关键词：
摘要：
In this paper we discuss general tridiagonal matrix models which are natural extensions of the ones given in Dumitriu and Edelman (J. Math. Phys. 43(11): 5830-5847, 2002; J. Math. Phys. 47(11):5830-5847, 2006). 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. The methods involved are based on an elementary result on sequences of real numbers and a judicious counting of levels of paths.
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