Wednesday, October 26, 2022 - 09:00 in ZOOM - Video Conference
Finite size corrections to the random matrix limit of the distribution of the length of longest increasing subsequences
A talk in the Seminar Zufallsmatrizen series by
Folkmar Bornemann from TU München
| Abstract: |
In a seminal work, Baik/Deift/Johansson established in 1999 that a double scaling limit
tailored to the mode of the distribution of the length of longest increasing subsequences in
random distributions is given by the beta=2 Tracy-Widom distribution. Since the rate of
approximation is rather slow we improve upon this limit by two alternative approaches.
First, by a Stirling-type formula we get a numerically accessible approximation of the
discrete distribution itself and second, by analytic de-Poissonization (used in this context
for the first time), we establish formulas for the first two finite size corrections to the random
matrix limit. Both approaches are related to the concept of H-admissible entire functions
and the calculations (formula-wise and numerically) are based on representations of
generating functions in terms of operator determinants. We derive expansions of the
expected value and variance of the length distribution, exhibiting several more terms than
previously known.
Please contact Mario Kieburg (m.kieburg@unimelb.edu.au) for details regarding access.
Within the CRC this talk is associated to the project(s): C6 |
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