Limit theorems for linear eigenvalue statistics of overlapping matrices
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Publication:894184
DOI10.1214/EJP.V20-3937zbMATH Open1328.60013arXiv1407.4743MaRDI QIDQ894184
Publication date: 27 November 2015
Published in: Electronic Journal of Probability (Search for Journal in Brave)
Abstract: The paper proves several limit theorems for linear eigenvalue statistics of overlapping Wigner and sample covariance matrices. It is shown that the covariance of the limiting multivariate Gaussian distribution is diagonalized by choosing the Chebyshev polynomials of the first kind as the basis for the test function space. The covariance of linear statistics for the Chebyshev polynomials of sufficiently high degree depends only on the first two moments of the matrix entries. Proofs are based on a graph-theoretic interpretation of the Chebyshev linear statistics as sums over non-backtracking cyclic paths
Full work available at URL: https://arxiv.org/abs/1407.4743
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