$(2+1)$维随机表面生长中重正化累积量的稳态偏度和峰度
Steady-state skewness and kurtosis from renormalized cumulants in $(2+1)$-dimensional stochastic surface growth
摘要：
在自然界中，二维基底上表面的随机生长现象发生在各种情况下，其统计特性需要高阶累积量的研究。在这里，我们考虑由$(2+1)$维KPZ方程的平坦几何的高度波动的统计累积量。我们遵循一个图解方案，推导出重整化累积量的表达式，直到四阶定态。假设一个值的粗糙度指数从可靠的数值预测，我们计算第二，第三和第四累积量，产生偏度$S=0.2879$和峰度$Q=0.1995$。这些值与现有的数值估计吻合得很好。
英文摘要：
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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