Multicritical Scaling Limit of Shifted Schur Measure

TL;DR

This paper studies the scaling limits of shifted Schur measures, revealing a transition from Pfaffian to determinantal processes and identifying the higher-order Airy kernel as the limit.

Contribution

It explicitly determines the limit shape of strict partitions and proves the convergence to higher-order Airy kernel in the multicritical edge scaling limit.

Findings

Limit shape of strict partitions is explicitly determined.

Edge correlation functions converge to higher-order Airy kernel.

Transition from Pfaffian to determinantal point process is rigorously shown.

Abstract

We investigate the multicritical scaling limit of the shifted Schur measures. Under an appropriate scaling limit and specific conditions on the continuous parameters, we explicitly determine the limit shape of strict partitions distributed according to the shifted Schur measure. We then show that, under a multicritical condition, the edge scaling limit of the correlation function converges to a determinant of the higher-order Airy kernel. This rigorously demonstrates a transition from a Pfaffian point process to a determinantal distribution in the scaling limit.