The Scaling Limit Geometry of Near-Critical 2D Percolation |
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Authors: | Federico Camia Luiz Renato G Fontes Charles M Newman |
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Institution: | 1. Department of Mathematics, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands 2. Instituto de Matemática e Estatística, Universidade de S?o Paulo, Paulo, Italy 3. Courant Inst. of Mathematical Sciences, New York University, New York, USA
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Abstract: | We analyze the geometry of scaling limits of near-critical 2D percolation, i.e., for p = p
c+λδ1/ν, with ν = 4/3, as the lattice spacing δ → 0. Our proposed framework extends previous analyses for p = p
c, based on SLE
6. It combines the continuum nonsimple loop process describing the full scaling limit at criticality with a Poissonian process
for marking double (touching) points of that (critical) loop process. The double points are exactly the continuum limits of
“macroscopically pivotal” lattice sites and the marked ones are those that actually change state as λ varies. This structure
is rich enough to yield a one-parameter family of near-critical loop processes and their associated connectivity probabilities
as well as related processes describing, e.g., the scaling limit of 2D minimal spanning trees. |
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Keywords: | scaling limits percolation near-critical minimal spanning tree finite size scaling |
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