Gaussian Fluctuations for Random Matrices with Correlated Entries
Gaussian Fluctuations for Random Matrices with Correlated Entries
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 …