Gap probability for the hard edge Pearcey process

Abstract

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 the relevant Fredholm determinants. We establish an integral representation of the gap probability via a Hamiltonian related a system of coupled differential equations. Together with some remarkable differential identities for the Hamiltonian, we derive the large gap asymptotics for the thinned case, up to and including the constant term. As an application, we also obtain the asymptotic statistical properties of the counting function for the hard edge Pearcey process.

62 pages, 7 figures

References in corpus (4)

• Asymptotics of Tracy-Widom distributions and the total integral of a Painlevé II function
• Randomly incomplete spectra and intermediate statistics
• Non-intersecting squared Bessel paths and multiple orthogonal polynomials for modified Bessel weights
• Full counting statistics for interacting trapped fermions

Cited by in corpus (1)

• Asymptotics of the deformed higher order Airy-kernel determinants and applications