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arXiv · 2504.20721

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

Mattia Cafasso·Carla Mariana da Silva Pinheiro
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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.

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Mattia Cafasso, Carla Mariana da Silva Pinheiro. 2025-04-29. Unitary ensembles with a critical edge point, their multiplicative statistics and the Korteweg-de-Vries hierarchy. https://arxiv.org/abs/2504.20721

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