Asymptotics of the hard edge Pearcey determinant

Luming Yao; Lun Zhang

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arXiv · 2209.12524

Asymptotics of the hard edge Pearcey determinant

Luming Yao·Lun Zhang

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Abstract

We study the Fredholm determinant of an integral operator associated to the hard edge Pearcey kernel. This determinant appears in a variety of random matrix and non-intersecting paths models. By relating the logarithmic derivatives of the Fredholm determinant to a $3 \times 3$ Riemann-Hilbert problem, we obtain asymptotics of the determinant, which is also known as the large gap asymptotics for the corresponding point process.

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Luming Yao, Lun Zhang. 2022-09-26. Asymptotics of the hard edge Pearcey determinant. https://arxiv.org/abs/2209.12524

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