Smallest gaps between eigenvalues of real Gaussian matrices

Matthew Meeker; Patrick Lopatto

Smallest gaps between eigenvalues of real Gaussian matrices

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arxiv 2403.09521 v2 pith:6KWTC3MH submitted 2024-03-14 math.PR math-phmath.MP

Patrick Lopatto , Matthew Meeker This is my paper · ORCID

classification math.PRmath-phmath.MP

keywords eigenvaluesgapsgaussianrealsmallestasymptoticcomplexconsider

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abstract

We consider an $n\times n$ matrix of independent real Gaussian random variables and determine the asymptotic distribution of the smallest gaps between complex eigenvalues.

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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.

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