Reversibility of Whole-Plane SLE

الأصل · EN

The main result of this paper is that, for κ∈(0,4], whole-plane SLEκ satisfies reversibility, which means that the time-reversal of a whole-plane SLEκ trace is still a whole-plane SLEκ trace. In addition, we find that the time-reversal of a radial SLEκ trace for κ∈(0,4] is a disc SLEκ trace with a marked boundary point. The main tool used in this paper is a stochastic coupling technique, which is used to couple two whole-plane SLEκ traces so that they overlap. Another tool used is the Feynman-Kac formula, which is used to solve a PDE. The solution of this PDE is then used to construct the above coupling.