Scaling limit of DLA on a long line segment

Abstract

In this paper, we prove that the bulk of DLA starting from a long line segment on the $x$-axis has a scaling limit to the stationary DLA process (SDLA). 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.