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2012 Internal aggregation models on comb lattices
Wilfried Huss, Ecaterina Sava
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Electron. J. Probab. 17: 1-21 (2012). DOI: 10.1214/EJP.v17-1940


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.


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Wilfried Huss. Ecaterina Sava. "Internal aggregation models on comb lattices." Electron. J. Probab. 17 1 - 21, 2012.


Accepted: 12 April 2012; Published: 2012
First available in Project Euclid: 4 June 2016

zbMATH: 1244.82047
MathSciNet: MR2915666
Digital Object Identifier: 10.1214/EJP.v17-1940

Primary: 60J10
Secondary: 05C81

Keywords: asymptotic shape , comb lattice , divisible sandpile , Growth model , internal diffusion limited aggregation , Random walk , rotor-router aggregation , rotor-router walk


Vol.17 • 2012
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