Weak convergence of the empirical spectral distribution of ultra-high-dimensional banded sample covariance matrices

2015/08/05 by Kamil Jurczak, Jurczak, Kamil
Engineering · Mathematics · #FOS: Mathematics #Mathematical Analysis and Transform Methods #Probability (math.PR) #Random Matrices and Applications #Sparse and Compressive Sensing Techniques #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1508.01101

openalex publication_date 2015/08/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this article we investigate high-dimensional banded sample covariance matrices under the regime that the sample size n, the dimension p and the bandwidth d tend simultaneously to infinity such that n/p→ 0 and 2d/n→ ygt;0. It is shown that the empirical spectral distribution of those matrices almost surely converges weakly to some deterministic probability measure which is characterized by its moments. Certain restricted compositions of natural numbers play a crucial role in the evaluation of the expected moments of the empirical spectral distribution.

Citations

• On the Distribution of the Roots of Certain Symmetric Matrices

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