# Averages of Products and Ratios of Characteristic Polynomials in Polynomial Ensembles

@article{Akemann2020AveragesOP,
title={Averages of Products and Ratios of Characteristic Polynomials in Polynomial Ensembles},
author={Gernot Akemann and Eugene Strahov and Tim R. W{\"u}rfel},
journal={Annales Henri Poincar{\'e}},
year={2020},
volume={21},
pages={3973 - 4002}
}
• Published 18 March 2020
• Mathematics
• Annales Henri Poincaré
Polynomial ensembles are a sub-class of probability measures within determinantal point processes. Examples include products of independent random matrices, with applications to Lyapunov exponents, and random matrices with an external field, that may serve as schematic models of quantum field theories with temperature. We first analyse expectation values of ratios of an equal number of characteristic polynomials in general polynomial ensembles. Using Schur polynomials, we show that polynomial…
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