16:00 -  17:00  F Camia (EURANDOM)


Continuum nonsimple loops and 2D critical percolation


Abstract: Substantial progress has been made in recent years on the
2D critical  percolation scaling limit and its conformal invariance
properties. In particular, chordal SLE6 (the Stochastic Loewner
Evolution with parameter k= 6) was, in the work of Schramm and of
Smirnov, identified as the scaling limit of the critical percolation
``exploration process.'' In this talk I will use that and other results
to construct what I will argue is the full scaling limit of the collection
of all closed contours surrounding the critical percolation clusters
on the 2D triangular lattice. 
This random process or gas of continuum nonsimple loops in the plane
is constructed inductively by repeated use of chordal SLE6. 
These loops do not cross but do touch each other --- indeed, any two
loops are connected by a finite ``path'' of touching loops. 
(Joint work with C. M. Newman.)