5 Spherical Asymptotics for the Rotor - Router Model in Z d
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چکیده
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 Zd, and use this to prove that the shape of the rotor-router aggregation model in Zd, suitably rescaled, converges to a Euclidean ball in Rd.
منابع مشابه
Spherical Asymptotics for the Rotor-Router Model in Z
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 Zd, and use this to prove that the shape of the rotor-router aggregation model in Zd, suitably ...
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تاریخ انتشار 2008