Limit theorems for linear eigenvalue statistics of overlapping matrices
Probability
2015-11-10 v3
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
Cite
@article{arxiv.1407.4743,
title = {Limit theorems for linear eigenvalue statistics of overlapping matrices},
author = {Vladislav Kargin},
journal= {arXiv preprint arXiv:1407.4743},
year = {2015}
}
Comments
44 pages, 4 figures, some typos are corrected and proofs clarified. Accepted to the Electronic Journal of Probability