Extreme eigenvalues of sparse, heavy tailed random matrices

Antonio Auffinger and Si Tang

Stochastic Processes and their Applications, 2016, vol. 126, issue 11, 3310-3330

Abstract: We study the statistics of the largest eigenvalues of p×p sample covariance matrices Σp,n=Mp,nMp,n∗ when the entries of the p×n matrix Mp,n are sparse and have a distribution with tail t−α, α>0. On average the number of nonzero entries of Mp,n is of order nμ+1, 0≤μ≤1. We prove that in the large n limit, the largest eigenvalues are Poissonian if α<2(1+μ−1) and converge to a constant in the case α>2(1+μ−1). We also extend the results of Benaych-Georges and Péché (2014) in the Hermitian case, removing restrictions on the number of nonzero entries of the matrix.

Keywords: Random matrices; Heavy tail; Sparse; Eigenvalue distribution (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:126:y:2016:i:11:p:3310-3330

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DOI: 10.1016/j.spa.2016.04.029

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