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.

arXiv comment3 figures, version published in Phys. Rev. E

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• A Renormalization Scheme and Skewness of Height Fluctuations in $(1+1)$-dimensional VLDS Dynamics
• Hyperskewness of $(1+1)$-dimensional KPZ Height Fluctuations
• Renormalized cumulants and velocity derivative skewness in Kolmogorov turbulence
• Steady-state skewness and kurtosis from renormalized cumulants in $(2+1)$-dimensional stochastic surface growth
• The Two Scaling Regimes of the Thermodynamic Uncertainty Relation for the KPZ-Equation