Limit theorems for linear eigenvalue statistics of overlapping matrices

2014/07/17 by Vladislav Kargin, Kargin, Vladislav
Computer Science · Mathematics · #Advanced Algebra and Geometry #Bayesian Methods and Mixture Models #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.1407.4743

openalex publication_date 2014/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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

Citations

• Central Limit Theorem for linear eigenvalue statistics of the Wigner and sample covariance random matrices
• Noncrossing partitions under rotation and reflection

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