Spectrum of Heavy-Tailed Elliptic Random Matrices

2020/10/03 by Campbell, Andrew, O'Rourke, Sean · 1 citation
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2010.01261

Abstract

An elliptic random matrix X is a square matrix whose (i,j)-entry X_ij is independent of the rest of the entries except possibly X_ji. Elliptic random matrices generalize Wigner matrices and non-Hermitian random matrices with independent entries. When the entries of an elliptic random matrix have mean zero and unit variance, the empirical spectral distribution is known to converge to the uniform distribution on the interior of an ellipse determined by the covariance of the mirrored entries. We consider elliptic random matrices whose entries fail to have two finite moments. Our main result shows that when the entries of an elliptic random matrix are in the domain of attraction of an α-stable random variable, for 0

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