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 text pdf 10.1512/iumj.2008.57.3022 10.1512/iumj.2008.57.3022 en Indiana Univ. Math. J. 57 (2008) 431 - 450 state-of-the-art mathematics http://iumj.org/access/