TY - JOUR
T1 - Height distribution of the Kardar-Parisi-Zhang equation with sharp-wedge initial condition
T2 - Numerical evaluations
AU - Prolhac, Sylvain
AU - Spohn, Herbert
PY - 2011/7/15
Y1 - 2011/7/15
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=79961113465&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.84.011119
DO - 10.1103/PhysRevE.84.011119
M3 - Article
AN - SCOPUS:79961113465
SN - 1539-3755
VL - 84
JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
IS - 1
M1 - 011119
ER -