Some Properties Of SLE_k(ρ) With Force Points On The Strip Domain

Stochastic Loewner evolution (SLEκ) describes a one-parameter κ family of conformally invariant random fractal curves constructed by solving the Loewner differential equation. For the study of SLEκ, general SLEκ is generalized to the case of SLEκ(ρ) with finite force points. The main work of this paper is as follows. First, we define SLEκ(ρ) with finite force points in the strip region and derive its existence and uniqueness, and the continuity of paths is proved. Secondly, we give martingale characterization of the strip SLEκ(p) with finite force points and discuss intersections of their paths. Thirdly, we discuss the couple relationship between the strip SLEκ(ρ) paths and the Gaussian free field, and the associated probability estimates are given.