*[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.]*

My understanding is that Schramm introduced the (radial) SLE in his 2000 paper to study the scaling limit of loop-erased random walk. Schramm’s ICM lecture also gives some further motivation (though not the original one) coming from Smirnov’s proof of conformal invariance of hexagonal percolation.

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