A Riemann Hilbert approach to the study of the generating function associated to the Pearcey process
Mathematical Physics
2023-05-10 v2 math.MP
Probability
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.
Keywords
Cite
@article{arxiv.2209.02411,
title = {A Riemann Hilbert approach to the study of the generating function associated to the Pearcey process},
author = {Thomas Chouteau},
journal= {arXiv preprint arXiv:2209.02411},
year = {2023}
}
Comments
18 pages, 3 figures