Two-dimensional scaling limits via marked nonsimple loops
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We postulate the existence of a natural Poissonian marking of the double (touching) points of SLE6 and hence of the related continuum nonsimple loop process that describes macroscopic cluster boundaries in 2D critical percolation. We explain how these marked loops should yield continuum versions of near-critical percolation, dynamical percolation, minimal spanning trees and related plane filling curves, and invasion percolation. We showthat this yields for some of the continuum objects a conformal covariance property that generalizes the conformal invariance of critical systems. It is an open problem to rigorously construct the continuum objects and to prove that they are indeed the scaling limits of the corresponding lattice objects.
Keywords:scaling limits percolation near-critical off-critical minimal spanning tree finite size scaling conformal covariance
Mathematical subject classification:Primary: 60K35 82B43 82B27 Secondary: 60G57 60K37 82B24 82B28
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