The height distribution of the KPZ equation with sharp wedge initial condition: numerical evaluations

Details The height distribution of the KPZ equation with sharp wedge initial condition: numerical evaluations The height distribution of the KPZ equation with sharp wedge initial condition: numerical evaluations

2011-05-02

arxiv.org/abs/1105.0383v2

Phys. Rev. E 84, 011119 (2011)

Physics

Condensed Matter

Statistical Mechanics

5 pages, 4 figures

Scientific paper

10.1103/PhysRevE.84.011119

The time-dependent probability distribution function of the height for the Kardar-Parisi-Zhang equation with sharp wedge initial conditions has been obtained recently as a convolution between the Gumbel distribution and a difference of two Fredholm determinants. We evaluate numerically this distribution over the whole time span. The crossover from the short time behavior, which is Gaussian, to the long time behavior, which is governed by the GUE Tracy-Widom distribution, is clearly visible.

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