Universal cusp scaling in random partitions

被引：0
作者：
Taro Kimura
Ali Zahabi
机构：
[1] Université de Bourgogne,Institut de Mathématiques de Bourgogne
[2] CNRS,undefined
[3] London Institute for Mathematical Sciences,undefined
[4] Royal Institution,undefined
来源：
Letters in Mathematical Physics | / 114卷
关键词：
Random partitions; Determinantal point process; Schur measures; cusp scaling limit; Isomonodromic system; 60B20; 05E10; 60G20; 82B27;
D O I：
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摘要：
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.
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