Stationary DLA is Well Defined

In this paper, we construct an infinite stationary diffusion limited aggregation (SDLA) on the upper half planar lattice, growing from an infinite line, with local growth rate proportional to the stationary harmonic measure. This model was suggested by Itai Benjamini. The main issue is a known problem in DLA models, the long range effects of large arms. In this paper we overcome this difficulty via a multi-scale argument controlling the dynamical discrepancies created on all scales while running two coupled SDLA on different starting configurations.