Scaling limit of DLA on a long line segment

Abstract

In this paper, we prove that the bulk of 2-dimensional DLA starting from a long line segment on the x 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.