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arXiv · 2606.00330

Singular central limit theorems for the spherical ensemble and beyond

Djalil Chafaï·David García-Zelada·Yuan Yuan Xu
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Abstract

We study the fluctuations of logarithmic Green singularities in the spherical ensemble, viewed as a random discretization of the two-sphere. Smooth observables exhibit the usual Sobolev or Gaussian free field fluctuations, whereas logarithmic singularities live on a larger logarithmic scale and asymptotically decouple in high-dimension, producing an explicit white-noise limit. The result gives precise asymptotics for logarithmic potentials and characteristic polynomials, with constants expressed through chordal geometry on the sphere.

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Djalil Chafaï, David García-Zelada, Yuan Yuan Xu. 2026-05-29. Singular central limit theorems for the spherical ensemble and beyond. https://arxiv.org/abs/2606.00330

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