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.

arXiv comment62 pages, 7 figures

References in corpus (24)

• Level-Spacing Distributions and the Airy Kernel
• Determinantal random point fields
• Level-Spacing Distributions and the Bessel Kernel
• Universal singularity at the closure of a gap in a random matrix theory
• Level Spacing of Random Matrices in an External Source
• Large n limit of Gaussian random matrices with external source, Part III: Double scaling limit
• Asymptotics of Tracy-Widom distributions and the total integral of a Painlevé II function
• A note on biorthogonal ensembles
• Randomly incomplete spectra and intermediate statistics
• Non-intersecting squared Bessel paths and multiple orthogonal polynomials for modified Bessel weights
• Multicritical edge statistics for the momenta of fermions in non-harmonic traps
• Large deformations of the Tracy-Widom distribution I. Non-oscillatory asymptotics
• Counting statistics for non-interacting fermions in a $d$-dimensional potential
• On the analysis of incomplete spectra in random matrix theory through an extension of the Jimbo-Miwa-Ueno differential
• Full counting statistics for interacting trapped fermions
• Large Complex Correlated Wishart Matrices: The Pearcey Kernel and Expansion at the Hard Edge
• Non-intersecting squared Bessel paths: critical time and double scaling limit
• Fredholm determinant solutions of the Painlevé II hierarchy and gap probabilities of determinantal point processes
• Asymptotics of Fredholm determinant associated with the Pearcey kernel
• Nonlinear PDEs for gap probabilities in random matrices and KP theory
• Large gap asymptotics for the generating function of the sine point process
• The hard edge tacnode process and the hard edge Pearcey process with non-intersecting squared Bessel paths
• Gap probabilities for the Generalized Bessel process: a Riemann-Hilbert approach
• Critical behavior in Angelesco ensembles

Cited by in corpus (1)

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