Brownian web is what we now call the Brownian web. Formally speaking, it is a collection of one-dimensional coalescing Brownian motions starting from every space-time point in formula_1. The fact that the Brownian web consists of an "uncountable" number of Brownian motions is what makes the construction highly non-trivial. Arratia gave a construction but was unable to prove convergence of coalescing random walks to a limiting object and characterize such a limiting object. Tóth and Werner in their study of the true self-repelling motion obtained many detailed properties of this limiting object and its dual but did not prove convergence of coalescing
Schramm–Loewner evolution evolution is a probability measure on planar curves, given as the image of Wiener measure under this map. In general the curve γ need not be simple, and the domain "D" is not the complement of γ([0,"t"]) in "D", but is instead the unbounded component of the complement. There are two versions of SLE, using two families of curves, each depending on a non-negative real parameter κ: SLE depends on a choice of Brownian motion on the boundary of the domain, and there are several variations depending on what sort of Brownian motion is used: for example it might start