= Hugo Duminil-Copin
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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.<A new proof of the sharpness of the phase transition for Bernoulli percolation on Zd by Hugo Duminil-Copin and Vincent Tassion>[Abstract and Theorem 1.1]{ref}
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