A Short Proof of the Harris–Kesten Theorem
By Béla Bollobás, Oliver Riordan. 2004
75 citations recorded by the source corpus.
We give a short proof of the fundamental result that the critical probability for bond percolation in the planar square lattice Z2 is equal to 1/2. The lower bound was proved by Harris, who showed in 1960 that percolation does not occur at p = 1/2. The other, more difficult, bound was proved by Kesten, who showed in 1980 that percolation does occur for any p > 1/2. 2000 Mathematics Subject Classification 60K35, 82B43.
Subfields: Condensed Matter Physics, Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/1558ed723ddc6f341fd2b5249ba794062f88ecc6
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In Condensed Matter Physics
In Mathematical Physics
In Statistics and Probability
Citations in the corpus
- Sharp phase transition for the random-cluster and Potts models via decision trees (2017, background): “It was also proved for percolation on self-dual polygon configurations in [BR06].”
- Influence and sharp-threshold theorems for monotonic measures (2005, methodology): “4) have been used in [5] to obtain a further proof that the critical probability pc of bond percolation on the square lattice satisfies pc = (1)2 .”