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Large gaps of CUE and GUE

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arxiv 1807.02149 v3 pith:QIZHAWRZ submitted 2018-07-05 math.PR

classification math.PR
keywords gapsarticleclassicaldensitiesdistributionsgivengumbellarge
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In this article, we study the largest gaps of the classical random matrices of CUE and GUE, and show that after rescaling, the limiting densities are given by the Gumbel distributions.

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Cited by 2 Pith papers

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

  1. Smallest gaps of the two-dimensional Coulomb gas

    math.PR 2025-07 conditional novelty 7.0 of 10

    For a general potential, the smallest gaps of the 2D Coulomb gas at beta=2 are of order n^{-3/4} and converge to a Poisson point process with intensity determined by the equilibrium density.

  2. Private Low-Rank Approximation for Covariance Matrices, Dyson Brownian Motion, and Eigenvalue-Gap Bounds for Gaussian Perturbations

    cs.DS 2025-02 reject novelty 4.0 of 10

    The paper claims an improved differentially private rank-k covariance approximation via complex Gaussian noise and Dyson Brownian motion, but its real-part output can have rank up to 2k, so the main theorem as stated ...

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