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.
*December 10, 1961 – September 1, 2008
†Supported by the European Research Council AG CONFRA, the Swiss National Science Foundation, and by the Chebyshev Laboratory (Faculty of Mathematics and Mechanics, St. Petersburg State University) under the grant of the government of the Russian Federation
AMS 2000 subject classifications: Primary 60K35; secondary 28C20, 82B43, 60G60
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Schramm*, O., Smirnov†, S., Garban, C. (2011). On the Scaling Limits of Planar Percolation. In: Benjamini, I., Häggström, O. (eds) Selected Works of Oded Schramm. Selected Works in Probability and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9675-6_35
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