Scaling limits of anisotropic Hastings-Levitov clusters

DOI10.1214/10-AIHP395zbMath1251.82025arXiv0908.0086MaRDI QIDQ2428952

Fredrik Johansson Viklund, Amanda G. Turner, Alan A. Sola

Publication date: 22 April 2012

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0908.0086

zbMATH Keywords

scaling limitsLoewner differential equationboundary flowanisotropic growth models

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Interacting random processes; statistical mechanics type models; percolation theory (60K35) General theory of conformal mappings (30C35) Interface problems; diffusion-limited aggregation arising in equilibrium statistical mechanics (82B24) Limit theorems in probability theory (60F99)

Related Items (21)

Directed, cylindric and radial Brownian webs ⋮ Large deviations of Schramm-Loewner evolutions: a survey ⋮ Dima Khavinson's 60th: a summary of open problems in analysis and mathematical physics ⋮ Scaling limits for planar aggregation with subcritical fluctuations ⋮ Scaling limits of anisotropic growth on logarithmic time-scales ⋮ The Loewner–Kufarev energy and foliations by Weil–Petersson quasicircles ⋮ Loewner chains and evolution families on parallel slit half-planes ⋮ Stability of regularized Hastings-Levitov aggregation in the subcritical regime ⋮ Large deviations of radial \(SLE_{\infty}\) ⋮ Tightness results for infinite-slit limits of the chordal Loewner equation ⋮ Fluctuation results for Hastings-Levitov planar growth ⋮ Elementary examples of Loewner chains generated by densities ⋮ Hastings-Levitov aggregation in the small-particle limit ⋮ Small-particle limits in a regularized Laplacian random growth model ⋮ Ergodic theorems for random clusters ⋮ Limits of radial multiple SLE and a Burgers-Loewner differential equation ⋮ Loewner chains with quasiconformal extensions: an approximation approach ⋮ Multiple SLE and the complex Burgers equation ⋮ One-dimensional scaling limits in a planar Laplacian random growth model ⋮ Integrability-preserving regularizations of Laplacian Growth ⋮ Directed Diffusion-Limited Aggregation

Cites Work

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• Discrete Löwner evolution.
• Laplacian growth as one-dimensional turbulence
• Ergodic theorems for random clusters
• Weak convergence of the localized disturbance flow to the coalescing Brownian flow
• Some remarks on Laplacian growth
• Aggregation in the plane and Loewner's equation.

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