Wednesday, January 30, 2019 - 16:00 in V3-201
On Kac polynomials and truncations of random orthogonal matrices
A talk in the Seminar Zufallsmatrizen series by
Mihail Poplavskyi from King's College London
| Abstract: |
Zeros of random polynomials give a rise to a point process
which does look similar to the ones arising in RMT but has no integrable
structure. We discuss a long standing problem of finding persistence
probability asymptotic behaviour for the family of Kac polynomials of
even large degree. We first use imprecise connection to the model of
truncations of random orthogonal matrices and calculate persistence
probability by using integrability of corresponding RMT model. We then
present recent progress in solving another integrable model, namely
Gaussian Stationary Process with sech correlations, which was shown in
2002 [Dembo, Poonen, Shao, Zeitouni] to give a precise approximation for
Kac polynomials. The talk is based on joint works with M. Gebert
(QMUL/UC Davis), G. Schehr (LPTMS).
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