Fluctuations for internal DLA on the comb

摘要

We study internal diffusion limited aggregation (DLA) on the two dimensional comb lattice. The comb lattice is a spanning tree of the Euclidean lattice, and internal DLA is a random growth model, where simple random walks, starting one at a time at the origin of the comb, stop when reaching the first unoccupied site. An asymptotic shape is suggested by a lower bound of Huss and Sava (Electron. J. Probab. 17 (2012) 30). We bound the fluctuations with respect to this shape.