Scaling limit of DLA on a long line segment
Scaling limit of DLA on a long line segment
复制标题
长线段上 DLA 的缩放限制
DOI：
10.1090/tran/8771
复制
发表时间：
2022
影响因子：
1.3
通讯作者：
Yuan Zhang
中科院分区：
文献类型：
--
作者：
Yingxin Mu;Eviatar B. Procaccia;Yuan Zhang
在本文中，我们证明了从x轴上的长线段开始的二维DLA的体积对静止DLA有缩放限制。主要的现象学困难是多尺度、非单调的相互作用。我们通过两个过程之间的耦合方案和具有吸收介观边界段的中间DLA过程来克服这一点。我们的结果允许将结果从更适合的无限固定DLA过程导入到更物理的有限聚集。
In this paper, we prove that the bulk of 2-dimensional DLA starting from a long line segment on the x-axis has a scaling limit to the stationary DLA. The main phenomenological difficulty is the multi-scale, non-monotone interaction of the DLA arms. We overcome this via a coupling scheme between the two processes and an intermediate DLA process with absorbing mesoscopic boundary segments. Our result allows to import results from the more amenable infinite stationary DLA process to the more physical finite aggregations.