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

Published 17 Nov 2021 in math-ph, math.MP, and math.PR | (2111.09200v1)

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 Painlev\'e II hierarchy we define, together with its Lax pair.

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