Wednesday, July 19, 2023 - 09:00 in ZOOM - Video Conference
Biorthogonal polynomials related to disordered wires
A talk in the Seminar Zufallsmatrizen series by
Dong Wang from University of Chinese Academy of Sciences
| Abstract: |
The quantum transport problem for $1$ dimensional disordered wires can
be modeled by the Dorokhov-Mello-Pereyra Kumar (DMPK) equation that is
similar to the Dyson Brownian motion, and if the time-reversal symmetry is
broken, the DMPK equation has a free fermion solution, which is, after
taking the metallic limit, a biorthogonal ensemble. The biorthogonal
ensemble has the form $\prod_{1 \leq i < j \leq n} (x_i - x_j)(f(x_i) - f(x_j))
\prod^n_{i =1} x^{\alpha}_i e^{-nV(x_i)}, \quad f(x) = \sinh^2(\sqrt{x}).$ It is a
determinantal point process, and the correlation kernel can be expressed
by biorthogonal polynomials. In this talk we discuss an approach to the
Plancherel-Rotach type asymptotics of the biorthogonal polynomials by
vector Riemann-Hilbert problems.
Please contact Lucas Hackl
(Lucas.Hackl@unimelb.edu.au) for details regarding access
Within the CRC this talk is associated to the project(s): C6 |
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