2013/10/09 by Zhan, Dapeng
#FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.1310.2573
We first prove that, for κ∈(0,4), a whole-plane SLE(κ;κ+2) trace stopped at a fixed capacity time satisfies reversibility. We then use this reversibility result to prove that, for κ∈(0,4), a chordal SLEκ curve stopped at a fixed capacity time can be mapped conformally to the initial segment of a whole-plane SLE(κ;κ+2) trace. A similar but weaker result holds for radial SLEκ. These results are then used to study the ergodic behavior of an SLE curve near its tip point at a fixed capacity time. The proofs rely on the symmetry of backward SLE laminations and conformal removability of SLEκ curves for κ∈(0,4).