Computing the Loewner driving process of random curves in the half plane
arXiv:math/0702071 · doi:10.1007/s10955-008-9535-x
Abstract
We simulate several models of random curves in the half plane and numerically compute their stochastic driving process (as given by the Loewner equation). Our models include models whose scaling limit is the Schramm-Loewner evolution (SLE) and models for which it is not. We study several tests of whether the driving process is Brownian motion. We find that just testing the normality of the process at a fixed time is not effective at determining if the process is Brownian motion. Tests that involve the independence of the increments of Brownian motion are much more effective. We also study the zipper algorithm for numerically computing the driving function of a simple curve. We give an implementation of this algorithm which runs in a time O(N^1.35) rather than the usual O(N^2), where N is the number of points on the curve.
20 pages, 4 figures. Changes to second version: added new paragraph to conclusion section; improved figures cosmetically
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- Fractal iso-contours of passive scalar in smooth random flows
- Loewner driving functions for off-critical percolation clusters
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- Search for conformal invariance in compressible two-dimensional turbulence
- Stochastic Loewner Evolution