A generalisation of Schramm's formula for SLE(2)
arXiv:0810.4503 · doi:10.1088/1742-5468/2009/02/P02033
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 (9)
- 2D growth processes: SLE and Loewner chains
- Conformal Field Theories of Stochastic Loewner Evolutions
- Dipolar SLEs
- The scaling limits of planar LERW in finitely connected domains
- The O(n) model on the annulus
- LERW as an example of off-critical SLEs
- On the mass transport by a Burgers velocity field
- SLE on doubly-connected domains and the winding of loop-erased random walks
- Models of Passive and Reactive Tracer Motion: an Application of Ito Calculus