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arXiv · 2209.02411

A Riemann Hilbert approach to the study of the generating function associated to the Pearcey process

Thomas Chouteau
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Abstract

Using Riemann-Hilbert methods, we establish a Tracy-Widom like formula for the generating function of the occupancy numbers of the Pearcey process. This formula is linked to a coupled vector differential equation of order three. We also obtain a non linear coupled heat equation. Combining these two equations we obtain a PDE for the logarithm of the the generating function of the Pearcey process.

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Thomas Chouteau. 2022-09-06. A Riemann Hilbert approach to the study of the generating function associated to the Pearcey process. https://doi.org/10.1007/s11040-023-09455-8

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