TITLE:
The Stochastic Coupling of SLE on the Strip Domain
AUTHORS:
Shenghua Zou
KEYWORDS:
Strip SLEk, SLEk Trace, Stochastic Coupling
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.8 No.9,
September
22,
2020
ABSTRACT: The main work of this paper is to discuss the stochastic coupling of stirp SLEk(k ∈ (0,4]) on the stirp region Sπ. By constructing a bounded continuous local martingale, we prove that when a certain ordinary differential equation is satisfied, there is a coupling of two strip SLEk traces in Sπ; one is from a to b; the other is from b to a, such that the two curves visit the same set of points.