A convergent (1)/(N) expansion for GUE

2016/09/14 by Offer Kopelevitch, Kopelevitch, Offer
Computer Science · Mathematics · Physics and Astronomy · #Electromagnetic Scattering and Analysis #FOS: Mathematics #Matrix Theory and Algorithms #Numerical methods for differential equations #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1609.04414

openalex publication_date 2016/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the asymptotic 1/N expansion for the averages of linear statistics of the GUE is convergent when the test function is an entire function of order two and finite type. This allows to fully recover the mean eigenvalue density function for finite N from the coefficients of the expansion thus providing a resummation procedure. As an intermediate result we compute the bilateral Laplace transform of the GUE reproducing kernel in the half-sum variable, generalizing a formula of Haagerup and Thorbjørnsen.

Citations

• On the Distribution of the Roots of Certain Symmetric Matrices

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