Disordered elastic interfaces display avalanche dynamics at the depinning transition. For short-range interactions, avalanches correspond to compact reorganizations of the interface well described by the depinning theory. For long-range elasticity, an avalanche is a collection of spatially disconnected clusters. In this Letter we determine the scaling properties of the clusters and relate them to the roughness exponent of the interface. The key observation of our analysis is the identification of a Bienaymé-Galton-Watson process describing the statistics of the number of clusters. Our work has concrete importance for experimental applications where the cluster statistics is a key probe of avalanche dynamics.

中文翻译：

---

在远距离相互作用下固定雪崩的空间聚类

无序的弹性界面在固定转变时显示雪崩动力学。对于短程相互作用，雪崩对应于由固定理论很好描述的界面的紧凑重组。对于远距离弹性，雪崩是空间上不连续的簇的集合。在这封信中，我们确定了簇的缩放性质，并将它们与界面的粗糙度指数相关联。我们分析的主要观察结果是确定Bienaymé-Galton-Watson过程的过程，该过程描述了簇数的统计数据。我们的工作对于实验应用具有特定的重要性，在这些应用中，簇统计是雪崩动力学的关键探查。