Sum rules via large deviations: polynomial potentials and multi-cut regime on the unit circle

Fabrice Gamboa; Jan Nagel; Alain Rouault

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arXiv · 2509.23814

Sum rules via large deviations: polynomial potentials and multi-cut regime on the unit circle

Fabrice Gamboa·Jan Nagel·Alain Rouault

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Abstract

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.

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Fabrice Gamboa, Jan Nagel, Alain Rouault. 2025-09-28. Sum rules via large deviations: polynomial potentials and multi-cut regime on the unit circle. https://arxiv.org/abs/2509.23814

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