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Article Dans Une Revue Electronic Journal of Probability Année : 2021

On the convergence of massive loop-erased random walks to massive SLE(2) curves

Résumé

Following the strategy proposed by Makarov and Smirnov in arXiv:0909.5377, we provide technical details for the proof of convergence of massive loop-erased random walks to the chordal mSLE(2) process. As no follow-up of arXiv:0909.5377 appeared since then, we believe that such a treatment might be of interest for the community. We do not require any regularity of the limiting planar domain $\Omega$ near its degenerate prime ends $a$ and $b$ except that $(\Omega^\delta,a^\delta,b^\delta)$ are assumed to be `close discrete approximations' to $(\Omega,a,b)$ near $a$ and $b$ in the sense of a recent work arXiv:1810.05608.

Dates et versions

hal-02612906 , version 1 (19-05-2020)

Identifiants

Citer

Dmitry Chelkak, Yijun Wan. On the convergence of massive loop-erased random walks to massive SLE(2) curves. Electronic Journal of Probability, 2021, 26 (none), ⟨10.1214/21-EJP615⟩. ⟨hal-02612906⟩
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