A Riemann Hilbert approach to the study of the generating function associated to the Pearcey process
arXiv:2209.02411 · doi:10.1007/s11040-023-09455-8
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.
arXiv comment18 pages, 3 figures
References in corpus (10)
- Level-Spacing Distributions and the Airy Kernel
- Determinantal random point fields
- Level Spacing of Random Matrices in an External Source
- The Pearcey Process
- Large n limit of Gaussian random matrices with external source, Part III: Double scaling limit
- PDEs for the joint distributions of the Dyson, Airy and Sine processes
- The transition between the gap probabilities from the Pearcey to the Airy process; a Riemann-Hilbert approach
- Nonlinear PDEs for gap probabilities in random matrices and KP theory
- Universal edge scaling in random partitions
- Gap probabilities for the Generalized Bessel process: a Riemann-Hilbert approach