TY  - JOUR
AB  - 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.
DA  - 2020
DO  - 10.1007/s00023-020-00963-9
LA  - eng
M2  - pages3973–4002
PY  - 2020
SN  - 1424-0637
SP  - pages3973–4002-
T2  - Annales Henri Poincaré: A Journal of Theoretical and Mathematical Physics
TI  - Averages of products and ratios of characteristic polynomials in polynomial ensembles
UR  - https://nbn-resolving.org/urn:nbn:de:0070-pub-29437768
Y2  - 2024-11-22T18:13:24
ER  -