Rate of Convergence for Cardy’s Formula

Author(s)
Nachmias, Asaf; Watson, Samuel S.; Mendelson, Dana Sydney
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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 e[superscript O(√log logR)] R[superscript -1/3] for the probability that the cluster at the origin in the half-plane has diameter R, improving the previously known estimate of R [superscript −1/3+o(1)].
Date issued
2014-05
URI
http://hdl.handle.net/1721.1/104926
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
Communications in Mathematical Physics
Publisher
Springer Berlin Heidelberg
Citation
Mendelson, Dana, Asaf Nachmias, and Samuel S. Watson. “Rate of Convergence for Cardy’s Formula.” Communications in Mathematical Physics 329.1 (2014): 29–56.
Version: Author's final manuscript
ISSN
0010-3616
1432-0916
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