Two-dimensional critical percolation

The full scaling limit

Federico Camia, Charles Newman

Research output: Contribution to journalArticle

Abstract

We use SLE 6 paths to construct a process of continuum nonsimple loops in the plane and prove that this process coincides with the full continuum scaling limit of 2D critical site percolation on the triangular lattice - that is, the scaling limit of the set of all interfaces between different clusters. Some properties of the loop process, including conformal invariance, are also proved.

Original languageEnglish (US)
Pages (from-to)1-38
Number of pages38
JournalCommunications in Mathematical Physics
Volume268
Issue number1
DOIs
StatePublished - Nov 2006

Fingerprint

Scaling Limit
continuums
scaling
invariance
Conformal Invariance
Triangular Lattice
Continuum Limit
Continuum
Path

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Two-dimensional critical percolation : The full scaling limit. / Camia, Federico; Newman, Charles.

In: Communications in Mathematical Physics, Vol. 268, No. 1, 11.2006, p. 1-38.

Research output: Contribution to journalArticle

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