Fredholm Determinant Solutions of the Painlevé II Hierarchy and Gap Probabilities of Determinantal Point Processes
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Publication:5006197
DOI10.1093/imrn/rnz168zbMath1489.60081arXiv1902.05595OpenAlexW2913688938MaRDI QIDQ5006197
Manuela Girotti, Tom Claeys, Mattia Cafasso
Publication date: 13 August 2021
Published in: International Mathematics Research Notices (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1902.05595
Random matrices (probabilistic aspects) (60B20) Integral operators (47G10) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)
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The Riemann-Hilbert approach to the generating function of the higher order Airy point processes ⋮ Higher Order Airy and Painlevé Asymptotics for the mKdV Hierarchy ⋮ Universal edge scaling in random partitions ⋮ Momenta spacing distributions in anharmonic oscillators and the higher order finite temperature Airy kernel ⋮ Gap probability for the hard edge Pearcey process ⋮ Multicritical random partitions ⋮ Classical group matrix models and universal criticality ⋮ Recursion relation for Toeplitz determinants and the discrete Painlevé II hierarchy ⋮ Asymptotics of the deformed higher order Airy-kernel determinants and applications ⋮ Interface fluctuations associated with split Fermi seas ⋮ A fully noncommutative Painlevé II hierarchy: Lax pair and solutions related to Fredholm determinants ⋮ A \(\bar{\partial}\)-steepest descent method for oscillatory Riemann-Hilbert problems
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