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Exact scaling functions for one-dimensional stationary KPZ growth

Michael Prähofer and Herbert Spohn

Date: March 29, 2003


We determine the stationary two-point correlation function of the one-dimensional KPZ equation through the scaling limit of a solvable microscopic model, the polynuclear growth model. The equivalence to a directed polymer problem with specific boundary conditions allows one to express the corresponding scaling function in terms of the solution to a Riemann-Hilbert problem related to the Painlevé II equation. We solve these equations numerically with very high precision and compare with the prediction of Colaiori and Moore  obtained from the mode coupling approximation.

Paper [PDF]


double precision tables (16 digits):
Accuracy of the decimal numbers in the following tables is about 100 digits:

Michael Prähofer