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Title:
Power law convergence of crossing probabilities for critical percolation
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Abstract:
Convergence of the Cardy-Smirnov observables is the crucial element of the famous proof of existence of the scaling limit of critical percolation on hexagonal lattice. I will describe a proof of the power law convergence of Cardy-Smirnov observables on arbitrary simply-connected planar domains. The proof works for the usual critical percolation on hexagonal lattice, as well as for some modified versions. I will also explain the relevance of this result for the investigation of the rate of convergence of the critical percolation to its scaling limit. This is a joint work with L. Chayes and H. K. Lei.
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