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.