*[Corrected, thanks – T.]*

Even more basic, is that the image Brownian motion under conformal transformation is a time change of Brownian motion. So this is like doing random walk in Polar Coodinates or some other very complicated grid network.

]]>I think the scaling limit of self-avoiding random walk is conjectured to be SLE_{8/3}, not SLE_{4/3}. See for example, https://en.wikipedia.org/wiki/Self-avoiding_walk

*[Corrected, thanks – T.]*

*[Corrected, thanks – T.]*