A learning roadmap to the Schramm-Loewner evolution (SLE) for the complex analyst 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
 A: As far as I'm aware, the most current in-depth book reference on SLE is Greg Lawler's book Conformally Invariant Processes in the Plane, a PDF of which is available here. From experience, SLE theory is extremely hard to grasp without a global understanding of what's going on, both on the complex analysis side and the probability side, in addition to its applications.
There's also a set of lecture notes from the PIMS summer school, more in the context of self-avoiding-walks. 
A: Nathanael Berestycki and James Norris have written up notes on SLE, based on a Part III (ie. masters level) lecture course at Cambridge.  http://www.statslab.cam.ac.uk/~james/Lectures/ 
I think they might partially match at least parts b) and c) of your requirements. Best, Alan. 
A: 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. 
A: You'll correct me if I'm mistaken, but it seems to me that Vincent Beffara's lecture notes might be just what you're searching for.

The goal of these lectures is to provide a self-contained introduction
  to SLE and related objects, but some motivation is needed before
  introducing SLE as such; so it seems natural to start with a quick
  review of a few two-dimensional discrete models. The focus of the first
  part will be, for each model, to arrive at the question of scaling
  limits as quickly as possible, and to justify conformal invariance
  where it is known to hold in the limit.    
In the second part we
  discuss Schramm’s insight that, under mild (and reasonable)
  assumptions in addition to conformal invariance, the limit has to be
  distributed as one of a one-parameter family of measures on curves,
  which he named Stochastic Loewner Evolutions. They are now universally
  known as Schramm-Loewner Evolutions. We give a precise definition of
  these random curves and present a few of their fundamental properties.

