Spherical asymptotics for the rotor-router model in $\mathbb{Z}^d$
L. LevineYuval Peres
60G5060J4582C24discrete Laplacianinternal diffusion limited aggregationisoperimetric inequalitygrowth modelorthoconvexityrearrangement inequalityrotor-router model
The rotor-router model is a deterministic analogue of random walk invented by Jim Propp. It can be used to define a deterministic aggregation model analogous to internal diffusion limited aggregation. We prove an isoperimetric inequality for the exit time of simple random walk from a finite region in $\mathbb{Z}^d$, and use this to prove that the shape of the rotor-router aggregation model in $\mathbb{Z}^d$, suitably rescaled, converges to a Euclidean ball in $\mathbb{R}^d$.
Indiana University Mathematics Journal
2008
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10.1512/iumj.2008.57.3022
10.1512/iumj.2008.57.3022
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Indiana Univ. Math. J. 57 (2008) 431 - 450
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