Time-reversal of multiple-force-point SLE${}_{\kappa }(\underline{\rho })$ with all force points lying on the same side

Abstract

We define intermediate SLE${}_{\kappa }(\underline{\rho })$ and reversed intermediate SLE${}_{\kappa }(\underline{\rho })$ processes using Appell-Lauricella multiple hypergeometric functions, and use them to describe the time-reversal of multiple-force-point chordal SLE${}_{\kappa }(\underline{\rho })$ curves in the case that all force points are on the boundary and lie on the same side of the initial point, and $\kappa$ and $\underline{\rho }=({\rho }_1,\dots ,{\rho }_m)$ satisfy that either $\kappa \in (0,4]$ and ${\sum }_{j=1}^k{\rho }_j>-2$ for all $1\le k\le m$, or $\kappa \in (4,8)$ and ${\sum }_{j=1}^k{\rho }_j\ge \frac{\kappa }{2}-2$ for all $1\le k\le m$.

69 pages, 4 figures. Added explanation and corrected mistakes according to the referee's comments. arXiv admin note: substantial text overlap with arXiv:1901.00254

References in corpus (3)

• Duality of Chordal SLE
• Two-curve Green's function for $2$-SLE: the boundary case
• Green's function for cut points of chordal SLE attached with boundary arcs

Cited by in corpus (1)

• Two-curve Green's function for $2$-SLE: the boundary case