title: Height distribution of the Kardar-Parisi-Zhang equation with sharp-wedge initial condition: numerical evaluations.
abstract: 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 Gaussian unitary ensemble (GUE) Tracy-Widom distribution, is clearly visible.
authors.affiliation: Zentrum Mathematik and Physik Department, Technische Universität München, D-85747 Garching, Germany.
authors.forename: Sylvain
authors.initials: S
authors.lastname: Prolhac
authors.forename: Herbert
authors.initials: H
authors.lastname: Spohn