Time-reversal of multiple-force-point SLEκ(ρ‾)_κ(\underlineρ) with all force points lying on the same side

preprint2021arXivOpen access

Abstract

We define intermediate SLEκ(ρ‾)_κ(\underlineρ) and reversed intermediate SLEκ(ρ‾)_κ(\underlineρ) processes using Appell-Lauricella multiple hypergeometric functions, and use them to describe the time-reversal of multiple-force-point chordal SLEκ(ρ‾)_κ(\underlineρ) curves in the case that all force points are on the boundary and lie on the same side of the initial point, and κκ and ρ‾=(ρ1,…,ρm)\underlineρ=(ρ_1,\dots,ρ_m) satisfy that either κ∈(0,4]κ\in(0,4] and ∑j=1kρj>−2\sum_{j=1}^k ρ_j>-2 for all 1≤k≤m1\le k\le m, or κ∈(4,8)κ\in(4,8) and ∑j=1kρj≥κ2−2\sum_{j=1}^k ρ_j\ge \fracκ{2}-2 for all 1≤k≤m1\le k\le m.

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