Limiting shapes for deterministic centrally seeded growth models

DOI10.1007/s10955-007-9450-6zbMath1139.82025arXivmath/0702450OpenAlexW2129689906MaRDI QIDQ2473374

Anne Fey-den Boer, Frank Redig

Publication date: 27 February 2008

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0702450

zbMATH Keywords

sandpile modellimiting shaperotor router model

Mathematics Subject Classification ID

Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics (82C20) Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics (82C41)

Related Items (8)

A growth model based on the arithmetic \(Z\)-game ⋮ A shape theorem for exploding sandpiles ⋮ A sandpile model for proportionate growth ⋮ A note on the Abelian sandpile in \(\mathbb Z^d\) ⋮ Growth rates and explosions in sandpiles ⋮ Pattern formation in growing sandpiles with multiple sources or sinks ⋮ Strong spherical asymptotics for rotor-router aggregation and the divisible sandpile ⋮ Discrete balayage and boundary sandpile

Cites Work

• Strong spherical asymptotics for rotor-router aggregation and the divisible sandpile
• Internal diffusion limited aggregation
• Goldbug variations
• On the identity of the sandpile group
• Subdiffusive fluctuations for internal diffusion limited aggregation
• The rotor-router shape is spherical
• Self-organized criticality
• Self-organized critical state of sandpile automaton models
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