Sharp Asymptotics for Arm Probabilities in Critical Planar Percolation
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220_2024_5028_ReferencePDF.pdf
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Author(s)
Du, Hang
Gao, Yifan
Li, Xinyi
Zhuang, Zijie
Date Issued
July 23, 2024
Journal
Communications in Mathematical Physics
Publisher
Springer Berlin Heidelberg
Citation
Du, H., Gao, Y., Li, X. et al. Sharp Asymptotics for Arm Probabilities in Critical Planar Percolation. Commun. Math. Phys. 405, 182 (2024).
Version
Author's final manuscript
Abstract
In this work, we consider critical planar site percolation on the triangular lattice and derive sharp estimates on the asymptotics of the probability of half-plane j-arm events for j ≥ 1 and planar (polychromatic) j-arm events for j > 1 , building upon a recent, not yet peer-reviewed result of Binder and Richards (Convergence rates of random discrete model curves approaching sle curves in the scaling limit. Preprint, 2020). These estimates greatly improve previous results and in particular answer (a large part of) a question of Schramm (ICM Proc., 2006).
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s00220-024-05028-0
