Hydrodynamical Limits and Geometric Measure Theory: Mean Curvature Limits from a Threshold Voter Model

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Abstract

We consider hydrodynamical limits for a simple threshold voter model for a microscopically evolving random interface. This model, which is a zero-temperature Ising model, was studied by Spohn in a 1 + 1 setting. The model leads to motion by a certain anisotropic mean curvature. Here we develop this model through some notions of geometric measure theory, dispensing with the 1 + 1 restriction.

Original languageEnglish (US)
Pages (from-to)421-455
Number of pages35
JournalJournal of Functional Analysis
Volume169
Issue number2
DOIs
StatePublished - Dec 20 1999

Keywords

  • Geometric measure theory
  • Hydrodynamical limits
  • Integral currents
  • Threshold voter model

ASJC Scopus subject areas

  • Analysis

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