English

Fluctuations for internal DLA on the Comb

Probability 2014-01-28 v2

Abstract

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. We show that fluctuations with respect to this shape are gaussian as in the one-dimensional lattice.

Cite

@article{arxiv.1309.3444,
  title  = {Fluctuations for internal DLA on the Comb},
  author = {Amine Asselah and Houda Rahmani},
  journal= {arXiv preprint arXiv:1309.3444},
  year   = {2014}
}

Comments

31 pages, 2 figures, many errors fixed after referee report

R2 v1 2026-06-22T01:26:32.980Z