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.
Arous, G. B., Tannenbaum, A., & Zeitoum, O. (2003). Stochastic approximations to curve-shortening flows via particle systems. Journal of Differential Equations, 195(1), 119–142. https://doi.org/10.1016/S0022-0396(03)00166-9