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Transfer operator approach to 1D random band matrices

Vienna Probability Seminar

Date
Monday, October 21, 2024 15:45 - 16:45
Speaker
Mariya Shcherbina (Institute of Low Temp. Physics, Kharkov)
Location
Central Bldg / O1 / Mondi 2 (I01.O1.008)
Series
Seminar/Talk
Tags
Mathematics and CS Seminar, mathematical_seminar_ics
Host
Laszlo Erdös, Jan Maas
Contact
Central building mondi1

We apply the SUSY method to derive integral representations for the correlation functions of characteristic polynomials of Hermitian and non-Hermitian random band matrices. The structure of the obtained formulas allows us to apply the transfer operator approach in the 1D case. Thus, the analysis of the correlation function is replaced by the spectral analysis of some non-self-adjoint integral operator. The results of the analysis give us an understanding of the mechanism of the transition from the "localized" to "delocalized spectral behavior of one-dimensional band matrices.


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