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arXiv · 2605.27222

Sobolev convergence of log-determinants for smooth Wigner matrices

Giorgio Cipolloni·Patrick Lopatto
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Abstract

We show that the fields emerging from the log-determinant and the eigenvalue counting function of smooth Wigner matrices converge in law to centered Gaussian, logarithmically correlated, random elements in every negative Sobolev space $H^{-s}$.

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Giorgio Cipolloni, Patrick Lopatto. 2026-05-26. Sobolev convergence of log-determinants for smooth Wigner matrices. https://arxiv.org/abs/2605.27222

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