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

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.

18 pages, 3 figures

References in corpus (3)

• The Pearcey Process
• PDEs for the joint distributions of the Dyson, Airy and Sine processes
• Universal edge scaling in random partitions

Cited by in corpus (1)

• Universal Cusp Scaling in Random Partitions