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By Hugo Duminil-Copin, Vincent Tassion.

Inspected preprint 8 October 2015, arXiv:1502.03051; original title has Z^d. Theorem 1.1 and section 2.1.

Hugo Duminil-Copin coauthored a proof of the sharp bond percolation transition with Vincent Tassion. Their nearest-neighbor lattice argument establishes exponential decay below the critical probability and a positive lower bound for the infinite-cluster probability above it. The result explains why the transition separates quantitatively different connectivity behavior.^[ref]