Title: Full Moebius invariance of conformal loop ensembles


The conformal loop ensembles (CLE) are random countably infinite collections 
of loops in the plane satisfying a set of axioms, most importantly, the 
conformal restriction property. The loops in CLE are Schramm--Loewner-
evolution-type curves. The CLEs were invented (in mathematics) to describe 
the scaling limits of collections of interfaces in planar statistical 
physics models, such as the Ising model or the percolation, at criticality. 
Recent results indeed establish this connection for the percolation and FK 
Ising models. In this talk, I'll extend the usual definition of simple CLEs 
in domains with a boundary to nested CLEs in the entire plane. Then 
I'll show that the CLE loops are inside-outside symmetric, which implies 
the full M?bius invariance of the plane CLEs and extends their definition 
and existence to those of the CLEs in the Riemann sphere.

This is a joint work with Wendelin Werner (ETH Zurich). 
DOI: http://dx.doi.org/10.1007/s00440-015-0647-3