Friday, May 24, 2013

1305.5526 (Christophe Garban et al.)

The scaling limits of near-critical and dynamical percolation    [PDF]

Christophe Garban, Gábor Pete, Oded Schramm
We prove that near-critical percolation and dynamical percolation on the triangular lattice $\eta \Tg$ have a scaling limit as the mesh $\eta \to 0$, in the "quad-crossing" space $\HH$ of percolation configurations introduced by Schramm and Smirnov in \cite{SchSm}. The proof essentially proceeds by "perturbing" the scaling limit of the critical model, using the pivotal measures studied in \cite{GPS2a}. Markovianity and conformal covariance of these new limiting objects are also established.
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