# On the generating function of the Pearcey process

@inproceedings{Charlier2021OnTG, title={On the generating function of the Pearcey process}, author={Christophe Charlier and Philippe Moreillon}, year={2021} }

The Pearcey process is a universal point process in random matrix theory. In this paper, we study the generating function of the Pearcey process on any number m of intervals. We derive an integral representation for it in terms of a Hamiltonian that is related to a system of 6 m + 2 coupled nonlinear equations. We also obtain asymptotics for the generating function as the size of the intervals get large, up to and including the constant term. This work generalizes some results of Dai, Xu and…

## 5 Citations

### Gap Probability for the Hard Edge Pearcey Process

- MathematicsAnnales Henri Poincaré
- 2023

The hard edge Pearcey process is universal in random matrix theory and many other stochastic models. This paper deals with the gap probability for the thinned/unthinned hard edge Pearcey process over…

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

- Mathematics
- 2022

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…

### Asymptotics of the deformed Fredholm determinant of the confluent hypergeometric kernel

- MathematicsStudies in Applied Mathematics
- 2022

In this paper, we consider the deformed Fredholm determinant of the confluent hypergeometric kernel. This determinant represents the gap probability of the corresponding determinantal point process…

### Exponential moments for disk counting statistics of random normal matrices in the critical regime

- MathematicsNonlinearity
- 2023

We obtain large n asymptotics for the m-point moment generating function of the disk counting statistics of the Mittag–Leffler ensemble, where n is the number of points of the process and m is…

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