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Journal of the European Mathematical Society

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Volume 20, Issue 5, 2018, pp. 1195–1268
DOI: 10.4171/JEMS/786

Published online: 2018-04-13

The scaling limits of near-critical and dynamical percolation

Christophe Garban[1], Gábor Pete[2] and Oded Schramm

(1) Université Lyon 1, Villeurbanne, France
(2) Technical University of Budpest and Hungarian Academy of Sciences, Budapest, Hungary

We prove that near-critical percolation and dynamical percolation on the triangular lattice $\eta \mathbb T$ have a scaling limit as the mesh $\eta$ tends to 0, in the “quad-crossing” space $\mathcal H$ 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.

Keywords: Statistical mechanics, percolation, dynamical percolation, critical and near-critical percolation, conformal invariance, scaling limit

Garban Christophe, Pete Gábor, Schramm Oded: The scaling limits of near-critical and dynamical percolation. J. Eur. Math. Soc. 20 (2018), 1195-1268. doi: 10.4171/JEMS/786