Universal Cusp Scaling in Random Partitions

TL;DR

This paper investigates the universal cusp scaling behavior of random partitions under the Schur measure, deriving higher-order kernels and differential equations to describe multi-critical phenomena.

Contribution

It extends previous work to include higher-order Pearcey kernels and analyzes gap probabilities and asymptotics in the cusp scaling limit.

Findings

Derived the higher-order Pearcey kernel for multi-critical behavior

Established coupled nonlinear differential equations for gap probabilities

Analyzed asymptotic behavior in the large gap limit

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.