Spatial Clustering of Depinning Avalanches in Presence of Long-Range Interactions

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