English

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.

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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