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General tridiagonal random matrix models, limiting distributions and fluctuations
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  • Published: 20 March 2008

General tridiagonal random matrix models, limiting distributions and fluctuations

  • Ionel Popescu1,2 

Probability Theory and Related Fields volume 144, pages 179–220 (2009)Cite this article

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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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Authors and Affiliations

  1. School of Mathematics, Georgia Institute of Technology, 686 Cherry Street, Atlanta, GA, 30332, USA

    Ionel Popescu

  2. IMAR, 21 Calea Grivitei Street, 010702, Bucharest, Sector 1, Romania

    Ionel Popescu

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  1. Ionel Popescu
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Correspondence to Ionel Popescu.

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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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  • Received: 15 November 2006

  • Revised: 26 January 2008

  • Published: 20 March 2008

  • Issue Date: May 2009

  • DOI: https://doi.org/10.1007/s00440-008-0145-y

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Keywords

  • Matrix Model
  • Random Matrice
  • Joint Moment
  • Eigenvalue Distribution
  • Tridiagonal Matrix
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