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Eigenvalue gaps of the Laplacian of random graphs

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arxiv 2501.00234 v2 pith:UYYY63T5 submitted 2024-12-31 math.PR math.CO

Nicholas Christoffersen , Kyle Luh , Hoi H. Nguyen , Jingheng Wang This is my paper
classification math.PRmath.CO
keywords laplaciandelocalizationgapsrandomaffinealongeffectiveeigenvalue
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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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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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    math.CA 2026-07 accept novelty 7.0 of 10

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