Spherical asymptotics for the rotor-router model in Zd

By Lionel Levine, Yuval Peres. 2005

48 citations recorded by the source corpus.

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 Z d , and use this to prove that the shape of the rotor-router aggregation model in Z d , suitably rescaled, converges to a Euclidean ball in R d .

Subfields: Condensed Matter Physics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/29d76a4263b4e1a4a7bdd7d9d09cf3f18479399d

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In Condensed Matter Physics

In Mathematical Physics

In Statistics and Probability

Citations in the corpus

Strong Spherical Asymptotics for Rotor-Router Aggregation and the Divisible Sandpile (2007, background): “Despite the impressive empirical evidence for circularity, the best result known until now [14] says only that if An is rescaled to have unit volume, the volume of the symmetric difference of An with a ball of unit volume tends to zero as a power of n, as n ↑ ∞.”
Rotor Walks and Markov Chains (2009, methodology): “se of rotor walk; see also [22].) A special case of results presented here was reported in [13], and earlier drafts of the current work provided partial inspiration for some of the recent progress in [3, 4, 5, 6, 8, 12, 17, 19, 18], which we discuss below. The idea of stack walks has its roots in Wi”