The Riemann-Hilbert approach to the generating function of the higher order Airy point processes

Abstract

We prove a Tracy-Widom type formula for the generating function of occupancy numbers on several disjoint intervals of the higher order Airy point processes. The formula is related to a new vector-valued Painlevé II hierarchy we define, together with its Lax pair.

arXiv comment16 pages, 1 figure