Convergence of loop erased random walks on a planar graph to a chordal \(\mathrm{SLE}(2)\) curve (Q740757)

Let \(B_t\) be a one-dimensional standard Brownian motion with \(B_0= 0\). A chordal Schramm- Loewner evolution with parameter \(\kappa>0\) (abbreviated as chordal SLE\(_\kappa\)) is the random family of conformal maps \(g_t\) obtained from the chordal Loewner equation \[ {\partial \over \partial t} g_t(z)={2\over g_t(z)-\sqrt{\kappa} B_t}, \;\;g_0(z)=z. \] In this paper, the author considers a loop erased random walk (LERW) on a planar graph in a similar setting to the paper [\textit{A. Yadin} and \textit{A. Yehudayoff}, Ann. Probab. 39, No. 4, 1243--1285 (2011; Zbl 1234.60036)] and shows that an LERW conditioned to connecting two boundary points in a simply connected domain converges to a chordal SLE\(_2\) curve.