Spherical asymptotics for the rotor-router model in $\mathbb{Z}^d$

DOI10.1512/iumj.2008.57.3022zbMath1139.60347arXivmath/0503251OpenAlexW2102663108MaRDI QIDQ5460081

Lionel Levine, Yuval Peres

Publication date: 2 May 2008

Published in: Indiana University Mathematics Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0503251

zbMATH Keywords

isoperimetric inequalityexit timeaggregation modelinternal diffusion limited aggregation

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Other physical applications of random processes (60K40) Probabilistic potential theory (60J45) Interface problems; diffusion-limited aggregation in time-dependent statistical mechanics (82C24)

Related Items (17)

Bounds on the cover time of parallel rotor walks ⋮ A growth model based on the arithmetic \(Z\)-game ⋮ Deterministic Random Walks for Rapidly Mixing Chains ⋮ Stretched exponential decay for subcritical parking times on ⋮ A sandpile model for proportionate growth ⋮ Proportionate growth in patterns formed in the rotor-router model ⋮ Spiral structures in the rotor-router walk ⋮ Deterministic random walks on the integers ⋮ Strong emergence of wave patterns on Kadanoff sandpiles ⋮ Pattern formation in growing sandpiles with multiple sources or sinks ⋮ The rotor-router model on regular trees ⋮ Deterministic walks with choice ⋮ Strong spherical asymptotics for rotor-router aggregation and the divisible sandpile ⋮ Fast Simulation of Large-Scale Growth Models ⋮ Infinite-step stationarity of rotor walk and the wired spanning forest ⋮ The rotor-router shape is spherical ⋮ Deterministic random walks on finite graphs

This page was built for publication: Spherical asymptotics for the rotor-router model in $\mathbb{Z}^d$