Abstract
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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Popescu, I. General tridiagonal random matrix models, limiting distributions and fluctuations. Probab. Theory Relat. Fields 144, 179–220 (2009). https://doi.org/10.1007/s00440-008-0145-y
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DOI: https://doi.org/10.1007/s00440-008-0145-y