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

Abstract

Following the strategy proposed by Makarov and Smirnov [23] in 2009 (see also [3,2] for theoretical physics arguments), 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 to [23] appeared since then, we believe that such a treatment might be of interest to the community. We do not require any regularity of the limiting planar domain near its degenerate prime ends a and b except that (Ω δ , a δ , b δ ) are assumed to be close discrete approximations to (Ω, a, b) near a and b in the sense of a recent work [12].

Hypergeometric SLE with $κ=8$: Convergence of UST and LERW in Topological Rectangles

“…We derive the formula (1.1) through discrete observable. The analysis on discrete harmonic function from [CW19] plays an important role. We then derive the conditional law of γ M given X M in Section 5.2.…”