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