Rate of Convergence for Cardy's Formula

Dana Mendelson*, Asaf Nachmias, Samuel S. Watson

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We show that crossing probabilities in 2D critical site percolation on the triangular lattice in a piecewise analytic Jordan domain converge with power law rate in the mesh size to their limit given by the Cardy-Smirnov formula. We use this result to obtain new upper and lower bounds of (Formula Presented) for the probability that the cluster at the origin in the half-plane has diameter R, improving the previously known estimate of R -1/3+o(1).

Original languageEnglish
Pages (from-to)29-56
Number of pages28
JournalCommunications in Mathematical Physics
Volume329
Issue number1
DOIs
StatePublished - Jul 2014
Externally publishedYes

Funding

FundersFunder number
National Science Foundation#6923910
Natural Sciences and Engineering Research Council of Canada

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