Natural parametrization of percolation interface and pivotal points

Nina Holden, Xinyi Li, Xin Sun

Research output: Contribution to journalArticlepeer-review


We prove that the interface of critical site percolation on the triangular lattice converges to SLE6 in its natural parametrization, where the discrete interface is parametrized such that each edge is crossed in one unit of time, while the limiting curve is parametrized by its 7/4-dimensional Minkowski content. We also prove that the scaling limit of counting measure on the pivotal points, which was proved to exist by Garban, Pete, and Schramm (J. Amer. Math. Soc. 26 (2013) 939-1024), is its 3/4-dimensional Minkowski content up to a deterministic multiplicative constant.

Original languageEnglish (US)
Pages (from-to)7-25
Number of pages19
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Issue number1
StatePublished - Feb 2021


  • Minkowski content
  • Natural parametrization
  • Percolation
  • Scaling limit

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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