On the convergence of massive loop-erased random walks to massive SLE(2) curves
| Autor: | Chelkak, Dmitry, Wan, Yijun |
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| Rok vydání: | 2019 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: minor updates; 36 pages, 3 figures |
| Databáze: | arXiv |
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