Subcritical multiplicative chaos and the characteristic polynomial of the C$β$E
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910545569906688 |
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| author | Lambert, Gaultier Najnudel, Joseph |
| author_facet | Lambert, Gaultier Najnudel, Joseph |
| contents | The goal of this article is to expand on the relationship between random matrix and multiplicative chaos theories using the integrability properties of the circular beta-ensembles. We give a comprehensive proof of the multiplicative chaos convergence for the characteristic polynomial and eigenvalue counting function of the circular beta-ensembles throughout the subcritical phase, including negative powers. This generalizes recent results in the unitary case, [NSW20,BF22], to any beta>0 and for the eigenvalue counting field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_19817 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Subcritical multiplicative chaos and the characteristic polynomial of the C$β$E Lambert, Gaultier Najnudel, Joseph Probability The goal of this article is to expand on the relationship between random matrix and multiplicative chaos theories using the integrability properties of the circular beta-ensembles. We give a comprehensive proof of the multiplicative chaos convergence for the characteristic polynomial and eigenvalue counting function of the circular beta-ensembles throughout the subcritical phase, including negative powers. This generalizes recent results in the unitary case, [NSW20,BF22], to any beta>0 and for the eigenvalue counting field. |
| title | Subcritical multiplicative chaos and the characteristic polynomial of the C$β$E |
| topic | Probability |
| url | https://arxiv.org/abs/2407.19817 |