JournalsjemsVol. 20, No. 5pp. 1195–1268

The scaling limits of near-critical and dynamical percolation

  • Christophe Garban

    Université Lyon 1, Villeurbanne, France
  • Gábor Pete

    Technical University of Budpest and Hungarian Academy of Sciences, Budapest, Hungary
  • Oded Schramm

The scaling limits of near-critical and dynamical percolation cover
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Abstract

We prove that near-critical percolation and dynamical percolation on the triangular lattice ηT\eta \mathbb T have a scaling limit as the mesh η\eta tends to 0, in the “quad-crossing” space H\mathcal H of percolation configurations introduced by Schramm and Smirnov. The proof essentially proceeds by “perturbing” the scaling limit of the critical model, using the pivotal measures studied in our earlier paper. Markovianity and conformal covariance of these new limiting objects are also established.

Cite this article

Christophe Garban, Gábor Pete, Oded Schramm, The scaling limits of near-critical and dynamical percolation. J. Eur. Math. Soc. 20 (2018), no. 5, pp. 1195–1268

DOI 10.4171/JEMS/786