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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.

MSC:

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

Citations:

Zbl 0616.60099
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