Perfect boundaries in rotor-router aggregation on cylinders

Abstract

We study a rotor-router version of the internal diffusion-limited aggregation introduced by J.Propp. The existing estimations of boundary fluctuations of the aggregation cluster show that they grow not faster than $O(\log r)$ with the cluster radius $r$. We consider the rotor-router internal DLA on the semi-infinite cylinder and prove a constant width of boundary fluctuations not depending on the radius of the cylinder.

14 pages, 3 figures

References in corpus (4)

• Sublogarithmic fluctuations for internal DLA
• From logarithmic to subdiffusive polynomial fluctuations for internal DLA and related growth models
• Orbits of rotor-router operation and stationary distribution of random walks on directed graphs
• A Loop Reversibility and Subdiffusion of the Rotor-Router Walk