Stochastic approximations to curve-shortening flows via particle systems

Gérard B. Arous, Allen Tannenbaum, Ofer Zeitoum

Research output: Contribution to journalArticle

Abstract

Curvature-driven flows have been extensively considered from a deterministic point of view. Besides their mathematical interest, they have been shown to be useful for a number of applications including crystal growth, flame propagation, and computer vision. In this paper, we describe a random particle system, evolving on the discretized unit circle, whose profile converges toward the Gauss-Minkowsky transformation of solutions of curve-shortening flows initiated by convex curves. Our approach may be considered as a type of stochastic crystalline algorithm. Our proofs are based on certain techniques from the theory of hydrodynamical limits.

Original languageEnglish (US)
Pages (from-to)119-142
Number of pages24
JournalJournal of Differential Equations
Volume195
Issue number1
DOIs
StatePublished - Nov 20 2003

Keywords

  • Curvature-driven flows
  • Curve shortening
  • Hydrodynamical limits
  • Interacting particle systems
  • Stochastic approximations

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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