Title: A SERIES OF INFORMAL DISCUSSIONS ON CONFORMAL LOOP ENSEMBLES
The goal of these series of very informal discussions.
is to go through two recent articles of Sheffield and Werner,
"Conformal Loop Ensembles: Construction via Loop-soups"
(http://arxiv.org/abs/1006.2373)
and
"Conformal Loop Ensembles: the Markovian Characterization"
(http://arxiv.org/abs/1006.2374). Before
starting with the articles we'll treat some background, and afterwards
we intend to discuss related topics.
The goal of the background discussions, which are likely to occupy more
than one meeting, is to introduce Brownian excursions, bubbles, loops
and loops soups - and to express the Radon-Nikodym derivative of chordal
SLE curves in different domains in terms of the Brownian loop soup. The
content is supposed to be rather elementary, but we allow ourselves to
make use of some Ito stochastic calculus, Girsanov's theorem, Loewner
chains and the definition of chordal SLE (at least after a brief
reminder of each).