@article{EJP1940,
author = {Wilfried Huss and Ecaterina Sava},
title = {Internal aggregation models on comb lattices},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {17},
year = {2012},
keywords = {growth model; comb lattice; internal diffusion limited aggregation; rotor-router aggregation; divisible sandpile; asymptotic shape; random walk; rotor-router walk},
abstract = {The two-dimensional comb lattice $\mathcal{C}_2$ is a natural spanning tree of the Euclidean lattice $\mathbb{Z}^2$. We study three related cluster growth models on $\mathcal{C}_2$: internal diffusion limited aggregation (IDLA), in which random walkers move on the vertices of $\mathcal{C}_2$ until reaching an unoccupied site where they stop; rotor-router aggregation in which particles perform deterministic walks, and stop when reaching a site previously unoccupied; and the divisible sandpile model where at each vertex there is a pile of sand, for which, at each step, the mass exceeding $1$ is distributed equally among the neighbours. We describe the shape of the divisible sandpile cluster on $\mathcal{C}_2$, which is then used to give inner bounds for IDLA and rotor-router aggregation.},
pages = {no. 30, 1-21},
issn = {1083-6489},
doi = {10.1214/EJP.v17-1940},
url = {http://ejp.ejpecp.org/article/view/1940}}