Wednesday, July 8, 2020 - 09:00 in ZOOM - Video Conference
Averaged characteristic polynomials in polynomial ensembles: determinantal formulas and universality
A talk in the Seminar Zufallsmatrizen series by
Tim Robert Würfel
| Abstract: |
We consider a sub-class of probability measures within determinantal
point processes called polynomial ensembles. Examples of such ensembles 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 analyze expectation values of characteristic
polynomials to obtain determinantal formulas for quantities such as the correlation kernel.
This leads to the notion of invertibility in polynomial ensembles, which can be used to
derive determinantal formulas only depending on the number of characteristic polynomials.
The correlation kernels for two models, closely related to applications in effective field theory,
are derived via these formulas for finite N.
We perform large N asymptotic analysis of the two kernels and obtain universality results in form
of Bessel-type kernels.
For further information, please contact Prof. Dr. Gernot Akemann: akemann@physik.uni-bielefeld.de
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