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arXiv · 1101.5820

On the scaling limits of planar percolation

Stanislav Smirnov·Oded Schramm
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Abstract

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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Stanislav Smirnov, Oded Schramm. 2011-01-30. On the scaling limits of planar percolation. https://doi.org/10.1214/11-aop659

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