# Gap Probability for the Hard Edge Pearcey Process

@article{Dai2022GapPF, title={Gap Probability for the Hard Edge Pearcey Process}, author={Dan Dai and Shuai‐Xia Xu and Lun Zhang}, journal={Annales Henri Poincar{\'e}}, year={2022}, pages={1-70} }

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 the interval (0, s ) by working on a $$3\times 3$$ 3 × 3 matrix-valued Riemann–Hilbert problem for the relevant Fredholm determinants. We establish an integral representation of the gap probability via the Hamiltonian related to a new system of coupled differential equations. Together with some…

## One Citation

### 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…

## References

SHOWING 1-10 OF 64 REFERENCES

### Hard-edge asymptotics of the Jacobi growth process

- MathematicsAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques
- 2020

We introduce a two parameter ($\alpha, \beta>-1$) family of interacting particle systems with determinantal correlation kernels expressible in terms of Jacobi polynomials $\{ P^{(\alpha, \beta)}_k…

### On the generating function of the Pearcey process

- Mathematics, Computer Science
- 2021

An integral representation for the generating function of the Pearcey process is derived in terms of a Hamiltonian that is related to a system of 6 m + 2 coupled nonlinear equations and asymptotics are obtained as the size of the intervals get large.

### Large Complex Correlated Wishart Matrices: The Pearcey Kernel and Expansion at the Hard Edge

- Mathematics
- 2016

We study the eigenvalue behaviour of large complex correlated Wishart matrices near an interior point of the limiting spectrum where the density vanishes (cusp point), and refine the existing results…

### The hard edge tacnode process and the hard edge Pearcey process with non-intersecting squared Bessel paths

- Mathematics
- 2014

A system of non-intersecting squared Bessel processes is considered which all start from one point and they all return to another point. Under the scaling of the starting and ending points when the…

### Gap Probabilities for the Generalized Bessel Process: A Riemann-Hilbert Approach

- Mathematics
- 2014

We consider the gap probability for the Generalized Bessel process in the single-time and multi-time case, a determinantal process which arises as critical limiting kernel in the study of…

### The hard-to-soft edge transition: Exponential moments, central limit theorems and rigidity

- MathematicsJournal of Approximation Theory
- 2022

### On the analysis of incomplete spectra in random matrix theory through an extension of the Jimbo–Miwa–Ueno differential

- MathematicsAdvances in Mathematics
- 2019