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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