  Stochastic Loewner evolution also called Schramm Loewner evolution
(abbreviated, SLE) is a rigorous tool in mathematics and statistical physics
for generating and studying scale invariant or fractal random curves in two
dimensions. The method is based on the older deterministic Loewner evolution
introduced by Karl Loewner, who demonstrated that an arbitrary curve not
crossing itself can be generated by a real function by means of a conformal
transformation. In 2000 Oded Schramm extended this method and demonstrated that
driving the Loewner evolution by a one-dimensional Brownian motion, the curves
in the complex plane become scale invariant; the fractal dimension turns out to
be determined by the strength of the Brownian motion. SLE fills a gap in our
understanding of the critical properties of a variety of lattice models in
their scaling limits and supplements the result obtained by means of conformal
field theory. In this paper we attempt to provide a simple and heuristic
discussion of some of the important aspects of SLE.
