Left passage probability of Schramm-Loewner Evolution.

SLE(k,p) is a variant of Schramm-Loewner Evolution (SLE) which describes the curves which are not conformal invariant, but are self-similar due to the presence of some other preferred points on the boundary. In this paper we study the left passage probability (LPP) of SLE(fc,p) through field theoretical framework and find the differential equation governing this probability. This equation is numerically solved for the special case K = 2 and hp = 0 in which hp is the conformal weight of the boundary changing (bcc) operator. It may be referred to loop erased random walk (LERW) and Abelian sandpile model (ASM) with a sink on its boundary. For the curve which starts from fo and conditioned by a change of boundary conditions at x0, we find that this probability depends significantly on the factor xo -- £o- We also present the perturbative general solution for large x0. As a prototype, we apply this formalism to SLE0k,k -- 6) which governs the curves that start from and end on the real axis. [ABSTRACT FROM AUTHOR]