From logarithmic to subdiffusive polynomial fluctuations for internal DLA and related growth models

DOI10.1214/12-AOP762zbMath1283.60117arXiv1009.2838OpenAlexW3105924170MaRDI QIDQ373571

Alexandre Gaudillière, Amine Asselah

Publication date: 17 October 2013

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1009.2838

zbMATH Keywords

random walkcluster growthshape theoreminternal diffusion limited aggregationlogarithmic fluctuationssubdiffusive fluctuations

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Probabilistic potential theory (60J45) Interface problems; diffusion-limited aggregation arising in equilibrium statistical mechanics (82B24)

Related Items (21)

Formation of an interface by competitive erosion ⋮ Laplacian growth and sandpiles on the Sierpiński gasket: limit shape universality and exact solutions ⋮ Competitive erosion is conformally invariant ⋮ Sublogarithmic fluctuations for internal DLA ⋮ Internal diffusion-limited aggregation with uniform starting points ⋮ Perfect boundaries in rotor-router aggregation on cylinders ⋮ Formation of large-scale random structure by competitive erosion ⋮ Scaling limits of fluctuations of extended-source internal DLA ⋮ Growing in time IDLA cluster is recurrent ⋮ The bi-dimensional directed IDLA forest ⋮ Internal DLA on cylinder graphs: fluctuations and mixing ⋮ Laplacian growth, sandpiles, and scaling limits ⋮ Internal DLA and the Gaussian free field ⋮ Lower bounds on fluctuations for internal DLA ⋮ Fluctuation results for Hastings-Levitov planar growth ⋮ The limiting shape for drifted internal diffusion limited aggregation is a true heat ball ⋮ From fractals in external DLA to internal DLA on fractals ⋮ Fast Simulation of Large-Scale Growth Models ⋮ How far do activated random walkers spread from a single source? ⋮ How long does it take for internal DLA to forget its initial profile? ⋮ Discrete balayage and boundary sandpile

Cites Work

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• Sublogarithmic fluctuations for internal DLA
• Internal DLA in higher dimensions
• Strong spherical asymptotics for rotor-router aggregation and the divisible sandpile
• Internal diffusion limited aggregation
• Internal diffusion-limited aggregation: parallel algorithms and complexity
• Goldbug variations
• Subdiffusive fluctuations for internal diffusion limited aggregation
• Fast Simulation of Large-Scale Growth Models
• Logarithmic fluctuations for internal DLA
• Random Walk: A Modern Introduction

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