More General Initial Conditions and Their Asymptotics

Abstract

Besides the three basic initial conditions analyzed in the previous two chapters, a further class of natural initial measures is obtained by first restricting the basic measures to a half-space and then joining pairwise. They all satisfy an asymptotic theorem, where the limit process is given by a crossover Airy process, which interpolates between two of the processes Airy$_2$, Airy$_1$ and Airy$_\text {stat}$. All the results can be further generalized to bounded modifications of the discussed initial conditions, as well as to asymptotics along space-like paths instead of just at a fixed time.