The harmonic explorer and its convergence to SLE(4)

有质量SLE$_4$与有质量调和探索子的标度极限

Massive SLE$_4$ and the scaling limit of the massive harmonic explorer

本文完整严格证明了有质量调和探索子的标度极限为共形协变、相对弦向SLE$_4$绝对连续的massive SLE$_4$，还证明合适边界条件下massive SLE$_4$可作为有质量高斯自由场的等值线耦合。

The rate of convergence of harmonic explorer to SLE4

Using the estimate of the difference between the discrete harmonic function and its corresponding continuous version we derive a rate of convergence of the Loewner driving function for the harmonic explorer to the Brownian motion with speed 4 on the real line. Based on this convergence rate, the derivative estimate for chordal $\mbox{SLE}_4$, and the estimate of tip structure modulus for harmonic explorer paths, we obtain an explicit power-law rate of convergence of the harmonic explorer paths to the trace of chordal $\mbox{SLE}_4$ in the supremum distance.

Harmonic measure and SLE

In this paper we rigorously compute the average multifractal spectrum of harmonic measure on the boundary of SLE clusters.

A Left passage explorer model

This is a short note describing a model generalizing the Harmonic explorer [6] that might be of interest and it is $\textit{not}$ intended for publication in a journal. The conjectured continuous model should have the same left-passage probability as SLE_$k$ but possibly be a different curve.

On Harmonic Measure of the Whole Plane Levy-Loewner Evolution

Levy-Loewner evolution (LLE) is a generalization of the Schramm-Loewner evolution (SLE) where the branching is possible in a course of growth process. We consider a class of radial Levy-Loewner evolutions for which sets of points of the average means beta-spectrum can be found exactly. In this paper we show how to overcome difficulties arised in previous works on multi-fractal analysis of SLE/LLE.

$SLE_6$ 与方格上的二维临界键渗流

$SLE_6$ and 2-d critical bond percolation on the square lattice

利用旋转不变性将 Smirnov 边 parafermionic 可观测量分解为两个新边可观测量，结合离散调和分析与共形映射，证明方格上二维临界键渗流探索路径在网格尺寸趋于零时收敛到 $SLE_6$ 的迹。