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 thinned/unthinned over interval $(0,s)$ by working on relevant Fredholm determinants. We establish an integral representation of via a Hamiltonian related system coupled differential equations. Together some remarkable identities Hamiltonian, we derive large asymptotics thinned case, up to including constant term. As application, also obtain asymptotic statistical properties counting function process.