Transition Analysis: From the Airy and Pearcey Kernels to the Sine Kernel
Classical Analysis and ODEs
2024-12-17 v1 Mathematical Physics
math.MP
Probability
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.
Keywords
Cite
@article{arxiv.2412.10596,
title = {Transition Analysis: From the Airy and Pearcey Kernels to the Sine Kernel},
author = {Thorsten Neuschel and Martin Venker},
journal= {arXiv preprint arXiv:2412.10596},
year = {2024}
}
Comments
29 pages, 7 figures