Stochastic approximations to curve-shortening flows via particle systems

  • Arous G
  • Tannenbaum A
  • Zeitoum O
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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. © 2003 Elsevier Inc. All rights reserved.

Author-supplied keywords

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

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  • Gérard B. Arous

  • Allen Tannenbaum

  • Ofer Zeitoum

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