Journal
LETTERS IN MATHEMATICAL PHYSICS
Volume 111, Issue 2, Pages -Publisher
SPRINGER
DOI: 10.1007/s11005-021-01389-y
Keywords
Random partition; Universal fluctuation; Multicritical point; Airy kernel; Tracy-Widom distribution; Gauge theory
Categories
Funding
- Investissements d'Avenir program
- Project ISITE-BFC [ANR-15-IDEX-0003]
- EIPHI Graduate School [ANR-17-EURE-0002]
- Bourgogne-Franche-Comte Region
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In this study, the universal edge scaling limit of random partitions with the Schur measure was established. The asymptotic behavior of the wave function, based on a Schrodinger-type differential equation, was explored. It was shown that in the edge scaling limit, the wave function generally approaches the Airy function and its higher-order analogs. Additionally, a higher-order Airy kernel and the Tracy-Widom distribution were constructed from the wave function in the scaling limit, with implications for multicritical phase transitions in large-size matrix models. The limit shape of random partitions was also discussed through semi-classical analysis of the wave function.
We establish the universal edge scaling limit of random partitions with the infinite-parameter distribution called the Schur measure. We explore the asymptotic behavior of the wave function, which is a building block of the corresponding kernel, based on the Schrodinger-type differential equation. We show that the wave function is in general asymptotic to the Airy function and its higher-order analogs in the edge scaling limit. We construct the corresponding higher-order Airy kernel and the Tracy-Widom distribution from the wave function in the scaling limit and discuss its implication to the multicritical phase transition in the large-size matrix model. We also discuss the limit shape of random partitions through the semi-classical analysis of the wave function.
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