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 language | English |
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Pages (from-to) | 29-56 |
Number of pages | 28 |
Journal | Communications in Mathematical Physics |
Volume | 329 |
Issue number | 1 |
DOIs | |
State | Published - Jul 2014 |
Externally published | Yes |
Funding
Funders | Funder number |
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National Science Foundation | #6923910 |
Natural Sciences and Engineering Research Council of Canada |