Gaussian fluctuations for random matrices with correlated entries

Details Gaussian fluctuations for random matrices with correlated entries Gaussian fluctuations for random matrices with correlated entries

2006-07-12

arxiv.org/abs/math-ph/0607028v1

Inter. Math. Res. Not. 2007 (2007), ID rmn047, 36 pages

Physics

Mathematical Physics

Scientific paper

10.1093/imrn/rnm047

For random matrix 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.

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