We give a self-contained and detailed presentation of Kesten's results 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.
"Near-critical percolation in two dimensions." Electron. J. Probab. 13 1562 - 1623, 2008. https://doi.org/10.1214/EJP.v13-565