Gaussian fluctuations for random matrices with correlated entries

Schulz-Baldes H, Schenker J (2007)

Publication Type: Journal article

Publication year: 2007

Journal

International Mathematics Research Notices Oxford University Press (OUP): Policy H - Oxford Open Option A

Publisher: Oxford University Press (OUP): Policy H - Oxford Open Option A

Book Volume: 15

Pages Range: 1-36

URI: http://de.arxiv.org/abs/math-ph/0607028

DOI: 10.1093/imrn/rnm047

Abstract

For randommatrix ensembles with non-gaussian matrix elements that may exhibit some correlations, it is shown that centered traces of polynomials in the matrix converge in distribution to a Gaussian process whose covariance matrix is diagonal in the basis of Chebyshev polynomials. The proof is combinatorial and adapts Wigner's argument showing the convergence of the density of states to the semicircle law. © The Author 2007.

Authors with CRIS profile

Hermann Schulz-Baldes Professur für Mathematik (Mathematische Physik)

Involved external institutions

Michigan State University US United States (USA) (US)

How to cite

APA:

Schulz-Baldes, H., & Schenker, J. (2007). Gaussian fluctuations for random matrices with correlated entries. International Mathematics Research Notices, 15, 1-36. https://dx.doi.org/10.1093/imrn/rnm047

MLA:

Schulz-Baldes, Hermann, and Jeffrey Schenker. "Gaussian fluctuations for random matrices with correlated entries." International Mathematics Research Notices 15 (2007): 1-36.

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