Schramm-Loewner Evolution

By Gregory F. Lawler. 2007

86 citations recorded by the source corpus.

This is the first expository set of notes on SLE I have written since publishing a book two years ago [45]. That book covers material from a year-long class, so I cannot cover everything there. However, these notes are not just a subset of those notes, because there is a slight change of perspective. The main differences are: o I have defined SLE as a finite measure on paths that is not necessarily a probability measure. This seems more natural from the perspective of limits of lattice systems and seems to be more useful when extending SLE to non-simply connected domains. (However, I do not discuss non-simply connected domains in these notes.) o I have made more use of the Girsanov theorem in studying corresponding martingales and local martingales. As in [45], I will focus these notes on the continuous process SLE and will not prove any results about convergence of discrete processes to SLE. However, my first lecture will be about discrete processes -- it is very hard to appreciate SLE if one does not understand what it is trying to model.

Subfields: Condensed Matter Physics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e34f3fd373422071bc497cd8d3dbc597f5cca8f3

Citations in the corpus

• Almost sure multifractal spectrum for the tip of an SLE curve (2009, unknown): “The chordal Schramm-Loewner evolution (SLEκ) is a one parameter family of probability measures on curves γ : [0, ∞) → H. It was invented by Oded Schramm [17] as a candidate for the scaling limit of lattice statistical physics models in two-dimensional that satisfy conformal invariance in the limit. ”