Wednesday, February 7, 2024 - 09:00 in ZOOM - Video Conference
Local hard edge universality of Muttalib-Borodin ensemble
A talk in the Seminar Zufallsmatrizen series by
Dong Wang from University of Chinese Academy of Science
| Abstract: |
Muttalib-Borodin ensemble is defined by the joint probability
density function $$\prod_{1 \leq i < j \leq n} (x_i - x_j)(x^{\theta}_i -
x^{\theta}_j) \prod^n_{i = 1} e^{-nV(x_i)}.$$ It is proposed by
physicist Muttalib as a toy model of quantum transport, and has
relations to random matrix theory. Because of its simplicity and its
non-trivial hard edge limit, the Muttalib-Borodin ensemble becomes
the archetype of biorthogonal ensembles. Borodin studied this model
in the $V(x) = x$ case, and found its limiting distribution around the
hard edge $0$. We show that for a large class of $V$, the Muttalib-
Borodin ensemble has the same limiting distribution, that is, the
model has a universal property. Our approach is by the
asymptomatic analysis of a kind of vector-valued Riemann-Hilbert
problem, with a new construction of the local parametrix for
irrational $\theta$.
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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