The full scaling limit of 2D critical percolation

Abstract: <br /> Substantial progress has been made in recent years on the 2D <br /> critical percolation scaling limit and its conformal invariance <br /> properties.In particular, chordal SLE_6 (the Stochastic Loewner <br /> Evolution with parameter 6) was, in the work of <br /> Schramm and of Smirnov, identified as <br /> the scaling limit of the critical percolation ``exploration process.'' <br /> In joint work with Federico Camia, we use that and other results to <br /> construct what we argue is the full scaling limit of the <br /> collection of all closed <br /> contours surrounding the critical percolation clusters on the 2D <br /> triangular lattice. <br /> This random process or gas of continuum nonsimple loops in <br /> the plane is constructed <br /> inductively by repeated use of chordal SLE_6. <br /> These loops do not cross but do touch each other --- <br /> indeed, any two loops are connected by a finite ``path'' of touching <br /> loops.