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Normal limit theorems for symmetric random matrices
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  • Published: November 1998

Normal limit theorems for symmetric random matrices

  • Eric M. Rains1 

Probability Theory and Related Fields volume 112, pages 411–423 (1998)Cite this article

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Abstract.

Using the machinery of zonal polynomials, we examine the limiting behavior of random symmetric matrices invariant under conjugation by orthogonal matrices as the dimension tends to infinity. In particular, we give sufficient conditions for the distribution of a fixed submatrix to tend to a normal distribution. We also consider the problem of when the sequence of partial sums of the diagonal elements tends to a Brownian motion. Using these results, we show that if O n is a uniform random n×n orthogonal matrix, then for any fixed k>0, the sequence of partial sums of the diagonal of O k n tends to a Brownian motion as n→∞.

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Authors and Affiliations

  1. AT&T Research, Room C290, 180 Park Avenue, Florham Park, NJ 07932-0971, USA. E-mail: rains@research.att.com, , , , , , US

    Eric M. Rains

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  1. Eric M. Rains
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Received: 3 February 1998 / Revised version: 11 June 1998

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Rains, E. Normal limit theorems for symmetric random matrices. Probab Theory Relat Fields 112, 411–423 (1998). https://doi.org/10.1007/s004400050195

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  • Issue Date: November 1998

  • DOI: https://doi.org/10.1007/s004400050195

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  • Mathematics Subject Classification (1991): Primary 15A52; Secondary 60F05
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