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

Abstract : 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.
Domain :

https://hal.archives-ouvertes.fr/hal-02612906
Contributor : Dmitry Chelkak <>
Submitted on : Tuesday, May 19, 2020 - 4:45:50 PM
Last modification on : Wednesday, May 20, 2020 - 1:41:26 AM

### Identifiers

• HAL Id : hal-02612906, version 1
• ARXIV : 1903.08045

### Citation

Dmitry Chelkak, Yijun Wan. On the convergence of massive loop-erased random walks to massive SLE(2) curves. 2020. ⟨hal-02612906⟩