Near-critical percolation in two dimensions. (English) Zbl 1189.60182

Summary: We give a self-contained and detailed presentation of H. Kesten’s results [Commun. Math. Phys. 109, 109–156 (1987; Zbl 0616.60099)] that allow to relate critical and near-critical percolation on the triangular lattice. They constitute an important step in the derivation of the exponents describing the near-critical behavior of this model. For future use and reference, we also show how these results can be obtained in more general situations, and we state some new consequences.


60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B43 Percolation
82B27 Critical phenomena in equilibrium statistical mechanics


Zbl 0616.60099
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