2020
DOI: 10.1007/s00023-020-00963-9
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Averages of Products and Ratios of Characteristic Polynomials in Polynomial Ensembles

Abstract: 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 ensembles constit… Show more

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Cited by 9 publications
(21 citation statements)
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References 46 publications
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“…Our results have only become possible due to recent mathematical developments in random matrix theory on so-called polynomial ensembles [49][50][51]. In the classical ensembles with unitary symmetry the repulsion between random matrix eigenvalues is given by the square of the Vandermonde determinant.…”
Section: Jhep12(2021)128mentioning
confidence: 97%
See 4 more Smart Citations
“…Our results have only become possible due to recent mathematical developments in random matrix theory on so-called polynomial ensembles [49][50][51]. In the classical ensembles with unitary symmetry the repulsion between random matrix eigenvalues is given by the square of the Vandermonde determinant.…”
Section: Jhep12(2021)128mentioning
confidence: 97%
“…One set of these remain to be polynomials, explaining the name of these ensembles. For certain subclasses of polynomial ensembles compact contour integral representations of the kernel are available [51], that allow for an asymptotic analysis.…”
Section: Jhep12(2021)128mentioning
confidence: 99%
See 3 more Smart Citations