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We prove that near-critical percolation and dynamical percolation on the triangular lattice have a scaling limit as the mesh tends to 0, in the “quad-crossing” space 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.
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Christophe Garban, Gábor Pete, Oded Schramm, The scaling limits of near-critical and dynamical percolation. J. Eur. Math. Soc. 20 (2018), no. 5, pp. 1195–1268DOI 10.4171/JEMS/786