Title: Conformal Loop Ensembles: The Markovian Characterization
Talk based on:
Scott Sheffield, Wendelin Werner
http://arxiv.org/abs/1006.2374
Abstract:
Conformal Loop Ensembles (CLE) are random collections of loops in a
planar domain and they are the conjectured scaling limits of the full
collections of interfaces of 2D lattice models of statistical physics
at criticality. The paper describes some consequences of the axiomatic
definition of Conformal Loop Ensembles (i.e. requiring conformal
invariance and a certain restriction property): the loop which
surrounds a given point can be seen as a SLE(kappa) bubble for some
value of kappa, and furthermore, this property holds for at most one
CLE. Therefore CLEs can be parametrized by kappa (if CLE exists for a
range of values of kappa, which is the subject of another
Sheffield&Werner paper). Finally, it is also shown in the paper that
every CLE has the same law as the random collections of loops defined
by the exploration tree construction of a branching SLE(kappa,kappa-6)
for some value of kappa.