The Riemann-Hilbert approach to the generating function of the higher order Airy point processes
Mathematical Physics
2021-11-18 v1 math.MP
Probability
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.
Keywords
Cite
@article{arxiv.2111.09200,
title = {The Riemann-Hilbert approach to the generating function of the higher order Airy point processes},
author = {Mattia Cafasso and Sofia Tarricone},
journal= {arXiv preprint arXiv:2111.09200},
year = {2021}
}
Comments
16 pages, 1 figure