Tail bounds for gaps between eigenvalues of sparse random matrices

Patrick Lopatto; Kyle Luh

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arXiv · 1901.05948

Tail bounds for gaps between eigenvalues of sparse random matrices

Patrick Lopatto·Kyle Luh

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Abstract

We prove the first eigenvalue repulsion bound for sparse random matrices. As a consequence, we show that these matrices have simple spectrum, improving the range of sparsity and error probability from the work of the second author and Vu. As an application of our tail bounds, we show that for sparse Erd\H{o}s--R\'enyi graphs, weak and strong nodal domains are the same, answering a question of Dekel, Lee, and Linial.

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Patrick Lopatto, Kyle Luh. 2019-01-17. Tail bounds for gaps between eigenvalues of sparse random matrices. https://arxiv.org/abs/1901.05948

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