Moments of C$β$E field partition function, $\mathsf{Sine}_β$ correlations and stochastic zeta
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915786372677632 |
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| author | Assiotis, Theodoros Najnudel, Joseph |
| author_facet | Assiotis, Theodoros Najnudel, Joseph |
| contents | We prove a conjecture of Fyodorov and Keating on the supercritical moments of the partition function of the C$β$E field or equivalently the supercritical moments of moments of the characteristic polynomial of the C$β$E ensemble for general $β>0$ and general real moment exponents. Moreover, we give the first expression for all correlation functions of the $\mathsf{Sine}_β$ point process for all $β>0$. The main object behind both results is the Hua-Pickrell stochastic zeta function introduced by Li and Valkó. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_08739 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Moments of C$β$E field partition function, $\mathsf{Sine}_β$ correlations and stochastic zeta Assiotis, Theodoros Najnudel, Joseph Probability Mathematical Physics We prove a conjecture of Fyodorov and Keating on the supercritical moments of the partition function of the C$β$E field or equivalently the supercritical moments of moments of the characteristic polynomial of the C$β$E ensemble for general $β>0$ and general real moment exponents. Moreover, we give the first expression for all correlation functions of the $\mathsf{Sine}_β$ point process for all $β>0$. The main object behind both results is the Hua-Pickrell stochastic zeta function introduced by Li and Valkó. |
| title | Moments of C$β$E field partition function, $\mathsf{Sine}_β$ correlations and stochastic zeta |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2602.08739 |