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.
Highlights
Stochastic Loewner evolution (SLE) is a family of random growth process introduced by Oded Schramm [1] to study the scaling limit of loop-erased random walk (LERW) and uniform spanning tree (UST)
It is closely related to the scale limit of the grid model in statistical physics
We prove that for κ ∈
Summary
Stochastic Loewner evolution (SLE) is a family of random growth process introduced by Oded Schramm [1] to study the scaling limit of loop-erased random walk (LERW) and uniform spanning tree (UST). It is closely related to the scale limit of the grid model in statistical physics. The scale limits of many two-dimensional systems are conjectured by theoretical physicists to be conformal invariant under critical conditions, but it has not been not proven by rigorous mathematical methods. On this basis, we prove that for κ ∈
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