The scaling limit geometry of near-critical 2D percolation

Federico Camia, Luiz Renato G. Fontes, Charles M. Newman

Research output: Contribution to journalArticle

Abstract

We analyze the geometry of scaling limits of near-critical 2D percolation, i.e., for p = pc+λδ1/ν, with ν = 4/3, as the lattice spacing δ → 0. Our proposed framework extends previous analyses for p = pc, based on SLE6. 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.

Original languageEnglish (US)
Pages (from-to)1155-1171
Number of pages17
JournalJournal of Statistical Physics
Volume125
Issue number5-6
DOIs
StatePublished - Dec 1 2006

    Fingerprint

Keywords

  • Finite size scaling
  • Minimal spanning tree
  • Near-critical
  • Percolation
  • Scaling limits

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this