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Corpus ID: 211252815

Eigenvector Statistics of L\'{e}vy Matrices

@article{Aggarwal2020EigenvectorSO,
title={Eigenvector Statistics of L\'\{e\}vy Matrices},
author={A. Aggarwal and Patrick Lopatto and J. Marcinek},
journal={arXiv: Probability},
year={2020}
}

We analyze statistics for eigenvector entries of heavy-tailed random symmetric matrices (also called Levy matrices) whose associated eigenvalues are sufficiently small. We show that the limiting law of any such entry is non-Gaussian, given by the product of a normal distribution with another random variable that depends on the location of the corresponding eigenvalue. Although the latter random variable is typically non-explicit, for the median eigenvector it is given by the inverse of a one… Expand