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Journal of Statistical Physics

, Volume 125, Issue 5–6, pp 1155–1171 | Cite as

The Scaling Limit Geometry of Near-Critical 2D Percolation

  • Federico Camia
  • Luiz Renato G. Fontes
  • Charles M. Newman
Article

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.

Keywords

scaling limits percolation near-critical minimal spanning tree finite size scaling 

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Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  • Federico Camia
    • 1
  • Luiz Renato G. Fontes
    • 2
  • Charles M. Newman
    • 3
  1. 1.Department of MathematicsVrije Universiteit AmsterdamAmsterdamThe Netherlands
  2. 2.Instituto de Matemática e EstatísticaUniversidade de São PauloPauloItaly
  3. 3.Courant Inst. of Mathematical SciencesNew York UniversityNew YorkUSA

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