Steady-state skewness and kurtosis from renormalized cumulants in (2  +  1)-dimensional stochastic surface growth. (17th October 2016)

• Record Type: Journal Article
• Authors: Singha, Tapas; Nandy, Malay K
• Is Part Of: Journal of statistical mechanics. (2016:Oct.)
• Publication Date: 2016-10-17
• Subjects: 9 -- 6 -- 12; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/2016/10/103204
• Languages: English
• ISSNs: 1742-5468

Abstract

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.