Unitary ensembles with a critical edge point, their multiplicative statistics and the Korteweg-de-Vries hierarchy

2025/04/29 by Cafasso, Mattia, Pinheiro, Carla Mariana da Silva · 2 citations
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2504.20721

Abstract

We study the multiplicative statistics associated to the limiting determinantal point process describing unitary random matrices with a critical edge point, where limiting density vanishes like a power 5/2. We prove that these statistics are governed by the first three equations of the KdV hierarchy, and study the asymptotic behavior of the relevant solutions.

Citations

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Cited by

• Asymptotic expansion for multiplicative statistics in a Hermitian matrix model connected to the lower tail of the KPZ equation
• Deformations of OP ensembles in a bulk critical scaling

Related

• Critical asymptotic behavior for the Korteweg-de Vries equation and in random matrix theory
• The Riemann-Hilbert approach to double scaling limit of random matrix eigenvalues near the "birth of a cut" transition
• Asymptotic expansion for multiplicative statistics in a Hermitian matrix model connected to the lower tail of the KPZ equation
• Critical edge statistics for deformed GinUEs
• Random matrix ensembles with singularities and a hierarchy of Painlev 'e\n III equations