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- W4300033503 abstract "The two-dimensional comb lattice $C_2$ is a natural spanning tree of the Euclidean lattice $mathbb{Z}^2$. We study three related cluster growth models on $C_2$: internal diffusion limited aggregation (IDLA), in which random walkers move on the vertices of $C_2$ 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 $C_2$, which is then used to give inner bounds for IDLA and rotor-router aggregation." @default.
- W4300033503 created "2022-10-03" @default.
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- W4300033503 date "2011-06-22" @default.
- W4300033503 modified "2023-09-26" @default.
- W4300033503 title "Internal Aggregation Models on Comb Lattices" @default.
- W4300033503 doi "https://doi.org/10.48550/arxiv.1106.4468" @default.
- W4300033503 hasPublicationYear "2011" @default.
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