We characterize universal features of the sample-to-sample fluctuations of global geometrical observables, such as the area, width, length, and center-of-mass position, in random growing planar clusters. Our examples are taken from simulations of both continuous and discrete models of kinetically rough interfaces, including several universality classes, such as Kardar-Parisi-Zhang. We mostly focus on the scaling behavior with time of the sample-to-sample deviation for those global magnitudes, but we have also characterized their histograms and correlations.

中文翻译：

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平面星团中全局几何测量的普遍涨落

我们描述了随机生长的平面簇中全局几何可观测量的样本间波动的普遍特征，例如面积、宽度、长度和质心位置。我们的示例取自动力学粗糙界面的连续和离散模型的模拟，包括几个通用类，例如 Kardar-Parisi-Zhang。我们主要关注这些全局量值的样本间偏差随时间的缩放行为，但我们也描述了它们的直方图和相关性。