Transition Analysis: From the Airy and Pearcey Kernels to the Sine Kernel

2024/12/13 by Thorsten Neuschel, Martin Venker, Neuschel, Thorsten +1
Engineering · Mathematics · #Fluid Dynamics and Turbulent Flows #Radiative Heat Transfer Studies #Gas Dynamics and Kinetic Theory

paper · pdf · doi:10.48550/arxiv.2412.10596

Abstract

We study transitions between the three universal limiting kernels Airy, Pearcey and sine kernel, arising in Random Matrix Theory at edge, cusp and bulk points of the spectrum. Under appropriate rescalings, we provide complete asymptotic expansions of the extended Airy kernel and the extended Pearcey kernel approaching the extended sine kernel, expliciting the fluctuations.

Related

• Transitions between critical kernels: from the tacnode kernel and critical kernel in the two-matrix model to the Pearcey kernel
• Asymptotics of the Airy-kernel determinant
• Operator level soft edge to bulk transition in β-ensembles via canonical systems
• Riemann-Hilbert approach to a generalised sine kernel
• Random skew plane partitions and the Pearcey process