Singular central limit theorems for the spherical ensemble and beyond
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911734972809216 |
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| author | Chafaï, Djalil García-Zelada, David Xu, Yuan Yuan |
| author_facet | Chafaï, Djalil García-Zelada, David Xu, Yuan Yuan |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2606_00330 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Singular central limit theorems for the spherical ensemble and beyond Chafaï, Djalil García-Zelada, David Xu, Yuan Yuan Probability Mathematical Physics 60B20, 60F05, 60G55, 82B21, 31C12 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. |
| title | Singular central limit theorems for the spherical ensemble and beyond |
| topic | Probability Mathematical Physics 60B20, 60F05, 60G55, 82B21, 31C12 |
| url | https://arxiv.org/abs/2606.00330 |