The Tacnode Kernel: Equality of Riemann–Hilbert and Airy Resolvent Formulas

DOI10.1093/imrn/rnv348zbMath1407.82036arXiv1211.4845OpenAlexW2962956782MaRDI QIDQ4619299

Steven Delvaux

Publication date: 6 February 2019

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1211.4845

zbMATH Keywords

Riemann-Hilbert problemFredholm determinantsBrownian motionsAiry integral operator

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Brownian motion (60J65) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Approximation by operators (in particular, by integral operators) (41A35) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Riemann-Hilbert problems in context of PDEs (35Q15) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) Dynamic critical phenomena in statistical mechanics (82C27)

Related Items (7)

Double interlacing in random tiling models ⋮ On the gap probability of the tacnode process ⋮ The tacnode Riemann-Hilbert problem ⋮ The \(k\)-tacnode process ⋮ Near-extreme eigenvalues and the first gap of Hermitian random matrices ⋮ Two Lax systems for the Painlevé II Equation, and Two Related Kernels in Random Matrix Theory ⋮ Tacnode GUE-minor processes and double Aztec diamonds

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