ON THE SCALING LIMITS OF PLANAR PERCOLATION BY ODED SCHRAMM1 AND STANISLAV SMIRNOV2 (WITH AN APPENDIX BY CHRISTOPHE GARBAN)

We prove Tsirelson’s conjecture that any scaling limit of the critical pla-nar percolation is a black noise. Our theorems apply to a number of percola-tion models, including site percolation on the triangular grid and any subse-quential scaling limit of bond percolation on the square grid. We also suggest a natural construction for the scaling limit of planar percolation, and more generally of any discrete planar model describing connectivity properties. 1. Introduction. 1.1. Motivation. This paper has a two-fold motivation: to propose a new con-struction for the (subsequential) scaling limits of the critical and near-critical per-colation in the plane, and to show that such limits are two-dimensional black noises as suggested by Boris Tsirelson