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arXiv · 1609.02547

Steady-state skewness and kurtosis from renormalized cumulants in $(2+1)$-dimensional stochastic surface growth

Tapas Singha·Malay K. Nandy
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Abstract

The phenomenon of stochastic growth of a surface on a two-dimensional substrate occurs in Nature in a variety of circumstances and its statistical characterization requires the study of higher order cumulants. Here, we consider the statistical cumulants of height fluctuations governed by the $(2+1)$-dimensional KPZ equation for flat geometry. We follow a diagrammatic scheme to derive the expressions for renormalized cumulants up to fourth order in the stationary state. Assuming a value for the roughness exponent from reliable numerical predictions, we calculate the second, third and fourth cumulants, yielding skewness $S=0.2879$ and kurtosis $Q=0.1995$. These values agree well with the available numerical estimations.

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Tapas Singha, Malay K. Nandy. 2016-09-08. Steady-state skewness and kurtosis from renormalized cumulants in $(2+1)$-dimensional stochastic surface growth. https://doi.org/10.1088/1742-5468/2016/10/103204

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