Fabrice Gamboa, Jan Nagel, Alain Rouault
Published 2023-01-23Version 1
We present correspondences induced by some classical mappings between measures on an interval and measures on the unit circle. More precisely, we link their sequences of orthogonal polynomial and their recursion coefficients. We also deduce some correspondences between particular equilibrium measures of random matrix ensembles. Additionally, we show that these mappings open up gateways between the sum rules associated with some classical models, leading to new formulations of several sum rules.
Large Deviations and Sum Rules for Spectral Theory - A Pedagogical Approach
Sum rules and large deviations for spectral measures on the unit circle
Asymptotic Results for Random Polynomials on the Unit Circle
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