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arXiv · 2501.00234

Eigenvalue gaps of the Laplacian of random graphs

Nicholas Christoffersen·Kyle Luh·Hoi H. Nguyen·Jingheng Wang
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Abstract

We show that, with very high probability, the random graph Laplacian has simple spectrum. Our method provides a quantitatively effective estimate of the spectral gaps. Along the way, we establish results on affine no-gaps delocalization, no-structure delocalization, overcrowding and small entries of the eigenvectors for the Laplacian model. These findings are of independent interest.

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Nicholas Christoffersen, Kyle Luh, Hoi H. Nguyen, Jingheng Wang. 2024-12-31. Eigenvalue gaps of the Laplacian of random graphs. https://arxiv.org/abs/2501.00234

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