Sharp asymptotics for arm probabilities in critical planar percolation

Hang Du; Yifan Gao; Xinyi Li; Zijie Zhuang

Sharp asymptotics for arm probabilities in critical planar percolation

Probability 2022-06-01 v1

Authors: Hang Du , Yifan Gao , Xinyi Li , Zijie Zhuang

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 $j \geq 1$ and planar (polychromatic) $j$ -arm events for $j>1$ . These estimates greatly improve previous results and in particular answer (a large part of) a question of Schramm (ICM Proc., 2006).

Keywords

percolation theory

Cite

@article{arxiv.2205.15901,
  title  = {Sharp asymptotics for arm probabilities in critical planar percolation},
  author = {Hang Du and Yifan Gao and Xinyi Li and Zijie Zhuang},
  journal= {arXiv preprint arXiv:2205.15901},
  year   = {2022}
}

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50 pages, 10 figures

Sharp asymptotics for arm probabilities in critical planar percolation

Abstract

Keywords

Cite

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