Stochastic Loewner evolution

In probability theory, stochastic Loewner evolution (SLE) is a one-parameter family of random conformally invariant curves in the plane. Invented by Oded Schramm in 1999, it is also known as Schramm-Loewner evolution. SLE was further developed by Greg Lawler, Oded Schramm and Wendelin Werner in a series of joint papers.

SLE is widely conjectured, and sometimes proved, to be the scaling limit of various critical percolation models, and other stochastic processes in the plane. The reference to Loewner acknowledges contributions in conformal geometry from the early part of the twentieth century of the Czech-American mathematician Charles Loewner (1893-1968).

Links

* Scaling limits of loop-erased random walks and uniform spanning trees Schramm's original paper, introducing SLE

* An Introduction to SLE by Lawler

* Random planar curves and Schramm-Loewner evolutions SLE survey by Werner