| Título: | Internal aggregation models on comb lattices |
| Autores: |
Huss, Wilfried; Vienna University of Technology Sava, Ecaterina; Graz University of Technology |
| Fecha: | 2012-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: | Peer-reviewed Article |
| Tema: |
growth model; comb lattice; internal diffusion limited aggregation; rotor-router aggregation; divisible sandpile; asymptotic shape; random walk; rotor-router walk 60J10; 05C81 |
| Descripción: | 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. |
| Idioma: | Inglés |
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