Kesten 1980: bond percolation on Z² has p_c = 1/2 exactly

Layer 1 — Physicsin the complex-systems subtree

Kesten 1980 (Comm. Math. Phys. 74:41) rigorous proof via self-duality. The dual of the square lattice is itself Z² (shifted by (1/2, 1/2)); a bond is open iff its dual bond is closed. Define θ(p) = probability that the origin belongs to…

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