Exact scaling functions for one-dimensional stationary KPZ growth

Details Exact scaling functions for one-dimensional stationary KPZ growth Exact scaling functions for one-dimensional stationary KPZ growth

2002-12-20

arxiv.org/abs/cond-mat/0212519v2

J. Stat. Phys. 115 (1-2), 255-279 (2004)

Physics

Condensed Matter

Statistical Mechanics

24 pages, 6 figures, replaced with revised version

Scientific paper

10.1023/B:JOSS.0000019810.21828.

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 Painleve II equation. We solve these equations numerically with very high precision and compare our, up to numerical rounding exact, result with the prediction of Colaiori and Moore [1] obtained from the mode coupling approximation.

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