Finite Rank Perturbation of Non-Hermitian Random Matrices: Heavy Tail and Sparse Regimes
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Author(s)
Han, Yi
Date Issued
September 29, 2025
Journal
Journal of Statistical Physics
Publisher
Springer US
Citation
Journal of Statistical Physics. 2025 Sep 29;192(10):136
Version
Author's final manuscript
Abstract
Abstract In this work we investigate spectral properties of squared random matrices with independent entries that have only two finite moments. We revisit the problem of perturbing a large, i.i.d. random matrix by a finite rank error. We prove that under a merely second moment condition, for a large class of perturbation matrix with bounded rank and bounded operator norm, the outlier eigenvalues of perturbed matrix still converge to that of the perturbation, which was previously known when matrix entries have finite fourth moment. We then show that the same perturbation holds for very sparse random matrices with i.i.d. entries, all the way up to a constant number of nonzero entries per row and column.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s10955-025-03517-7
