Averages of products and ratios of characteristic polynomials in polynomial ensembles

Akemann G, Strahov E, Würfel TR (2020)
Annales Henri Poincaré: A Journal of Theoretical and Mathematical Physics 21: pages3973–4002.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
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 constitute Giambelli compatible point processes, leading to a determinant formula for such ratios as in classical ensembles of random matrices. In the second part, we introduce invertible polynomial ensembles given, e.g. by random matrices with an external field. Expectation values of arbitrary ratios of characteristic polynomials are expressed in terms of multiple contour integrals. This generalises previous findings by Fyodorov, Grela, and Strahov. for a single ratio in the context of eigenvector statistics in the complex Ginibre ensemble.
Erscheinungsjahr
2020
Zeitschriftentitel
Annales Henri Poincaré: A Journal of Theoretical and Mathematical Physics
Band
21
Seite(n)
pages3973–4002
ISSN
1424-0637
eISSN
1424-0661
Finanzierungs-Informationen
Open-Access-Publikationskosten wurden durch die Universität Bielefeld im Rahmen des DEAL-Vertrags gefördert.
Page URI
https://pub.uni-bielefeld.de/record/2943776

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Akemann G, Strahov E, Würfel TR. Averages of products and ratios of characteristic polynomials in polynomial ensembles. Annales Henri Poincaré: A Journal of Theoretical and Mathematical Physics. 2020;21:pages3973–4002.
Akemann, G., Strahov, E., & Würfel, T. R. (2020). Averages of products and ratios of characteristic polynomials in polynomial ensembles. Annales Henri Poincaré: A Journal of Theoretical and Mathematical Physics, 21, pages3973–4002. doi:10.1007/s00023-020-00963-9
Akemann, G., Strahov, E., and Würfel, T. R. (2020). Averages of products and ratios of characteristic polynomials in polynomial ensembles. Annales Henri Poincaré: A Journal of Theoretical and Mathematical Physics 21, pages3973–4002.
Akemann, G., Strahov, E., & Würfel, T.R., 2020. Averages of products and ratios of characteristic polynomials in polynomial ensembles. Annales Henri Poincaré: A Journal of Theoretical and Mathematical Physics, 21, p pages3973–4002.
G. Akemann, E. Strahov, and T.R. Würfel, “Averages of products and ratios of characteristic polynomials in polynomial ensembles”, Annales Henri Poincaré: A Journal of Theoretical and Mathematical Physics, vol. 21, 2020, pp. pages3973–4002.
Akemann, G., Strahov, E., Würfel, T.R.: Averages of products and ratios of characteristic polynomials in polynomial ensembles. Annales Henri Poincaré: A Journal of Theoretical and Mathematical Physics. 21, pages3973–4002 (2020).
Akemann, Gernot, Strahov, Eugene, and Würfel, Tim Robert. “Averages of products and ratios of characteristic polynomials in polynomial ensembles”. Annales Henri Poincaré: A Journal of Theoretical and Mathematical Physics 21 (2020): pages3973–4002.
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arXiv: 2003.08128

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