Ergodicity of Stochastic Curve Shortening Flow in the Plane

2010/03/10 by Abdelhadi Es–Sarhir, Es-Sarhir, A., M.-K. von Renesse +1 · 3 citations
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Mathematical Biology Tumor Growth #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1003.2074

openalex publication_date 2010/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a model of the motion by mean curvature of an (1+1) dimensional interface in a 2D Brownian velocity field. For the well-posedness of the model we prove existence and uniqueness for certain degenerate nonlinear stochastic evolution equations in the variational framework of Krylov Rozovskii, replacing the standard coercivity assumption by a Lyapunov type condition. Ergodicity is established for the case of additive noise, using the lower bound technique for Markov semigroups by Komorowski, Peszat and Szarek

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• Stochastic Curve Shortening Flow with Scale-Dependent Noise
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