• Corpus ID: 235732196

On the generating function of the Pearcey process

  title={On the generating function of the Pearcey process},
  author={Christophe Charlier and Philippe Moreillon},
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… 

Figures from this paper

Gap Probability for the Hard Edge Pearcey Process

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

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

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

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

On the deformed Pearcey determinant



The Pearcey Process

The extended Airy kernel describes the space-time correlation functions for the Airy process, which is the limiting process for a polynuclear growth model. The Airy functions themselves are given by

The generating function for the Bessel point process and a system of coupled Painlevé V equations

We study the joint probability generating function for [Formula: see text] occupancy numbers on disjoint intervals in the Bessel point process. This generating function can be expressed as a Fredholm

Large gap asymptotics for the generating function of the sine point process

  • C. Charlier
  • Mathematics, Computer Science
    Proceedings of the London Mathematical Society
  • 2021
In this work, large gap asymptotics are obtained for the generating function of the sine point process, which are asymPTotics as the size of the intervals grows.

The Transition between the Gap Probabilities from the Pearcey to the Airy Process—a Riemann–Hilbert Approach

We consider the gap probability for the Pearcey and Airy processes; we set up a Riemann–Hilbert approach (different from the standard one) whereby the asymptotic analysis for large gap/large time of

Determinantal Point Processes

In this survey we review two topics concerning determinantal (or fermion) point processes. First, we provide the construction of diffusion processes on the space of configurations whose invariant

The Generating Function for the Airy Point Process and a System of Coupled Painlevé II Equations

For a wide class of Hermitian random matrices, the limit distribution of the eigenvalues close to the largest one is governed by the Airy point process. In such ensembles, the limit distribution of

The maximum deviation of the Sine β counting process

In this paper, we consider the maximum of the Sine β counting process from its expectation. We show the leading order behavior is consistent with the predictions of log–correlated Gaussian fields,

Corrigendum to: Exponential Moments and Piecewise Thinning for the Bessel Point Process

  • C. Charlier
  • Mathematics
    International Mathematics Research Notices
  • 2018
We obtain exponential moment asymptotics for the Bessel point process. As a direct consequence, we improve on the asymptotics for the expectation and variance of the associated counting function

PDEs for the Gaussian ensemble with external source and the Pearcey distribution

The Pearcey distribution is shown to satisfy a fourth-order PDE with cubic nonlinearity, which also gives the PDE for the transition probability of the Pearcey process, a limiting process associated with nonintersecting Brownian motions on R.