Skewness in (1+1)-dimensional Kardar-Parisi-Zhang-type growth

Abstract

We use the $(1+1)$-dimensional Kardar-Parisi-Zhang equation driven by a Gaussian white noise and employ the dynamic renormalization-group of Yakhot and Orszag without rescaling [J.~Sci.\ Comput.~{\bf 1}, 3 (1986)]. Hence we calculate the second and third order moments of height distribution using the diagrammatic method in the large scale and long time limits. The moments so calculated lead to the value $S=0.3237$ for the skewness. This value is comparable with numerical and experimental estimates.

3 figures, version published in Phys. Rev. E

References in corpus (2)

• Growing interfaces uncover universal fluctuations behind scale invariance
• An exact solution for the KPZ equation with flat initial conditions

Cited by in corpus (2)

• Steady-state skewness and kurtosis from renormalized cumulants in $(2+1)$-dimensional stochastic surface growth
• Renormalized cumulants and velocity derivative skewness in Kolmogorov turbulence