Universal Cusp Scaling in Random Partitions
Mathematical Physics
2024-02-06 v3 Statistical Mechanics
High Energy Physics - Theory
Combinatorics
math.MP
Probability
Abstract
We study the universal scaling limit of random partitions obeying the Schur measure. Extending our previous analysis [arXiv:2012.06424], we obtain the higher-order Pearcey kernel describing the multi-critical behavior in the cusp scaling limit. We explore the gap probability associated with the higher Pearcey kernel, and derive the coupled nonlinear differential equation and the asymptotic behavior in the large gap limit.
Cite
@article{arxiv.2208.07288,
title = {Universal Cusp Scaling in Random Partitions},
author = {Taro Kimura and Ali Zahabi},
journal= {arXiv preprint arXiv:2208.07288},
year = {2024}
}
Comments
41 pages, v2: presentation improved, typos corrected, v3: minor corrections