On the scaling limits of planar percolation

Details On the scaling limits of planar percolation On the scaling limits of planar percolation

2011-01-30

arxiv.org/abs/1101.5820v2

Annals of Probability 2011, Vol. 39, No. 5, 1768-1814

Mathematics

Probability

With an Appendix by Christophe Garban. Published in at http://dx.doi.org/10.1214/11-AOP659 the Annals of Probability (http:/

Scientific paper

10.1214/11-AOP659

We prove Tsirelson's conjecture that any scaling limit of the critical planar percolation is a black noise. Our theorems apply to a number of percolation models, including site percolation on the triangular grid and any subsequential scaling limit of bond percolation on the square grid. We also suggest a natural construction for the scaling limit of planar percolation, and more generally of any discrete planar model describing connectivity properties.

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