Universal cusp scaling in random partitions

We study the universal scaling limit of random partitions obeying the Schur measure. Extending our previous analysis (Kimura and Zahabi in Lett. Math. Phys. 111:48, 2021. https://doi.org/10.1007/s11005-021-01389-y), 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.