TITLE: A learning roadmap to the Schramm-Loewner evolution (SLE) for the complex analyst
QUESTION [13 upvotes]: I would like some good references to learn about the Schramm-Loewner evolution (SLE), for a complex analyst with no background in probability.
A quick google search gave a lot of references on SLE that are exactly the opposite of what I'm looking for, in the sense that they assume strong background in probability and no knowledge of complex analysis.
EDIT (In response to Timothy Chow's comment) :
I guess what I'm looking for is a reference that
(a) does not assume that the reader is familiar with the probability theory needed for SLE (except for the basics), so it should contain the required material on stochastic calculus, brownian motions, etc.
(b) describes in details the classical (non-stochastic) case
(c) contains an introduction to the stochastic case, which should focus more on the complex-analytic aspects than the probabilistic ones.
Thank you,
Malik

REPLY [5 votes]: I recall seeing this post half a year ago while I was searching for knowledge myself regarding the very same topic.
I thought I would throw my own master's dissertation into the picture.
It can be found by clicking here.
The aim while writing was to make a rigorous, self-contained and readable introduction to the SLE, for anybody who has obtained knowledge in advanced complex analysis and stochastic calculus. It is my guess that you will never find a rigorous text that does not assume familiarity with at least stochastic calculation on application-level. 
It treats compact hulls, and their relation to the Loewner equation. The overall method is taken directly from the brilliant notes written by Nathanael Berestycki and James Norris which may be found here. Then I introduce randomness through the Brownian motion, and present the proof of existence of the SLE trace, which was introduced in the article by Schramm & Rohde Annals Math. 161 (2005) 879-920. This may be the only part of my dissertation where the level of detail between my references and my own work is considerably different. Thus this may be the part that can save you some time.
I also include proofs of a "weak" phases characterization, which can be found in the Cambridge notes, among others. Finally, I discuss the simulation method presented by Tom Kennedy in his article J.Statist.Phys.128:1125-1137,2007
NB: I should of course stress that this is a master's dissertation and not an article from a journal, which means that it has not been through any approval-procedure apart from grading.