{"id":"hexagon/2610.00675","pdf":"https://hexagonmath.org/pdf/2610.00675v1","url":"https://hexagonmath.org/abs/2610.00675v1","tags":["msc:60B20","random matrix theory"],"score":0,"title":"Smallest Gaps between Eigenvalues of Wigner Matrices without Smoothness Assumptions","domain":"math.PR","origin":"ai-generated","source":"hexagon","authors":["Patrick Lopatto"],"reviews":0,"subject":"math.PR","summary":"We determine the asymptotic distribution of the smallest gaps between eigenvalues in the bulk of the spectrum of real symmetric Wigner matrices, including Bernoulli matrices. After multiplication by $N^{3/2}$, the gaps and their locations converge to a Poisson point process with the same intensity as for the Gaussian orthogonal ensemble. Since changing a single entry can move eigenvalues by an amount comparable to the smallest gaps, standard perturbative comparison estimates do not directly resolve this scale for arbitrary entry distributions. Instead, we use that resampling a few random…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-31","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}