Airy kernel determinant solutions to the KdV equation and integro-differential Painlevé equations

DOI10.1007/s00220-021-04108-9zbMath1477.37080arXiv2010.07723OpenAlexW3093390121WikidataQ115388553 ScholiaQ115388553MaRDI QIDQ2046796

Giulio Ruzza, Tom Claeys, Mattia Cafasso

Publication date: 19 August 2021

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.07723

zbMATH Keywords

second Painlevé equationintegro-differential equationKorteweg-de Vries equationKardar-Parisi-Zhang equation

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Integro-ordinary differential equations (45J05) KdV equations (Korteweg-de Vries equations) (35Q53) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Random matrices (algebraic aspects) (15B52) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Nonautonomous Hamiltonian dynamical systems (Painlevé equations, etc.) (37J65)

Related Items (10)

Momenta spacing distributions in anharmonic oscillators and the higher order finite temperature Airy kernel ⋮ Uniform tail asymptotics for Airy kernel determinant solutions to KdV and for the narrow wedge solution to KPZ ⋮ Generalized Gibbs ensemble of the Ablowitz-Ladik lattice, circular \(\beta\)-ensemble and double confluent Heun equation ⋮ Law of iterated logarithms and fractal properties of the KPZ equation ⋮ The Bessel kernel determinant on large intervals and Birkhoff's ergodic theorem ⋮ Integrability in the weak noise theory ⋮ Universality for multiplicative statistics of Hermitian random matrices and the integro-differential Painlevé II equation ⋮ Determinantal point processes conditioned on randomly incomplete configurations ⋮ Integrable equations associated with the finite‐temperature deformation of the discrete Bessel point process ⋮ On the integrable structure of deformed sine kernel determinants

Uses Software

• DLMF

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