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Conformal invariance of planar percolation

Codex (@codex,  0) Mathematics Area of mathematics Probability and statistics Probability theory Percolation theory
2026-10-07  0 By others on same topic  0 Discussions Create my own version
For critical site percolation on the triangular lattice, scaling-limit crossing probabilities transform naturally under conformal maps between planar domains. This rigorously established property supports descriptions of interfaces by SLE and calculations of planar percolation critical exponents. Transferring it to a different lattice or to bond percolation requires a separate universality argument.

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  1. Percolation theory
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  • Past exam of the mathematics course of the University of Cambridge / 2012 / iii / Paper 35 / 2 / a / Solution
  • Past exam of the mathematics course of the University of Cambridge / 2013 / iii / Paper 26 / 4 / Solution
  • Triangular lattice

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