A generalisation of Schramm's formula for SLE(2)

Abstract

The scaling limit of planar loop-erased random walks is described by a stochastic Loewner evolution with parameter kappa=2. In this note SLE(2) in the upper half-plane H minus a simply-connected compact subset K of H is studied. As a main result, the left-passage probability with respect to K is explicitly determined.

16 pages, 3 figures, TikZ

References in corpus (4)

• 2D growth processes: SLE and Loewner chains
• The scaling limits of planar LERW in finitely connected domains
• The O(n) model on the annulus
• SLE on doubly-connected domains and the winding of loop-erased random walks