Sum rules via large deviations: polynomial potentials and multi-cut regime on the unit circle
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914098934972416 |
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| author | Gamboa, Fabrice Nagel, Jan Rouault, Alain |
| author_facet | Gamboa, Fabrice Nagel, Jan Rouault, Alain |
| contents | Sum rules are elegant formulas that relate entropy functionals to coefficients associated with orthogonal polynomials [Sim11]. In a series of paper (see for example [GNR16], [GNR17], [BSZ18a], [BSZ18b]), interesting connections have been established between the large theory of spectral measures built on random matrices and sum rules. In this work, we extend this approach by studying sum rules within random matrix models with polynomial potentials on the unit circle, with a particular focus on cases where the equilibrium measure lacks full support. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_23814 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sum rules via large deviations: polynomial potentials and multi-cut regime on the unit circle Gamboa, Fabrice Nagel, Jan Rouault, Alain Probability Mathematical Physics 60F10, 60B20, 42C05, 47B15 Sum rules are elegant formulas that relate entropy functionals to coefficients associated with orthogonal polynomials [Sim11]. In a series of paper (see for example [GNR16], [GNR17], [BSZ18a], [BSZ18b]), interesting connections have been established between the large theory of spectral measures built on random matrices and sum rules. In this work, we extend this approach by studying sum rules within random matrix models with polynomial potentials on the unit circle, with a particular focus on cases where the equilibrium measure lacks full support. |
| title | Sum rules via large deviations: polynomial potentials and multi-cut regime on the unit circle |
| topic | Probability Mathematical Physics 60F10, 60B20, 42C05, 47B15 |
| url | https://arxiv.org/abs/2509.23814 |