Moments Match between the KPZ Equation and the Airy Point Process

Abstract

The results of Amir-Corwin-Quastel, Calabrese-Le Doussal-Rosso, Dotsenko, and Sasamoto-Spohn imply that the one-point distribution of the solution of the KPZ equation with the narrow wedge initial condition coincides with that for a multiplicative statistics of the Airy determinantal random point process. Taking Taylor coefficients of the two sides yields moment identities. We provide a simple direct proof of those via a combinatorial match of their multivariate integral representations.

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Cited by in corpus (19)

• The KPZ Limit of ASEP with Boundary
• Coulomb-gas electrostatics controls large fluctuations of the KPZ equation
• The ASEP and determinantal point processes
• Systematic time expansion for the Kardar-Parisi-Zhang equation, linear statistics of the GUE at the edge and trapped fermions
• Lower tail of the KPZ equation
• Simple derivation of the $(-\lambda H{)}^{5/2}$ tail for the 1D KPZ equation
• Airy kernel determinant solutions to the KdV equation and integro-differential Painlevé equations
• A Riemann-Hilbert approach to the lower tail of the KPZ equation
• Stochastic higher spin six vertex model and Madconald measures
• The lower tail of the half-space KPZ equation
• Uniform tail asymptotics for Airy kernel determinant solutions to KdV and for the narrow wedge solution to KPZ
• Lyapunov exponents of the half-line SHE
• Universality for multiplicative statistics of Hermitian random matrices and the integro-differential Painlevé II equation
• Airy Point Process via Supersymmetric Lifts
• The KPZ equation and moments of random matrices
• $x-y$ duality in Topological Recursion for exponential variables via Quantum Dilogarithm
• Large deviation bounds for the Airy point process
• Moments of the SHE under delta initial measure
• Identity between Restricted Cauchy Sums for the $q$-Whittaker and Skew Schur Polynomials