The tail of the crossing probability in near-critical percolation --- an appendix to Ahlberg & Steif [arXiv:1405.7144]

Gábor Pete

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arXiv · 1507.05522

The tail of the crossing probability in near-critical percolation --- an appendix to Ahlberg & Steif [arXiv:1405.7144]

Gábor Pete

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Abstract

We answer a question of Ahlberg and Steif (2014) by finding the tail behaviour of the crossing probability in near-critical planar percolation. Interestingly, this superexponentially small behaviour is different from the case of dynamical percolation, where the analogous tail probability was proved to be at least exponential and at most superpolynomial by Hammond, Mossel and Pete (2012). The proof is simple, given the scale covariance established by Garban, Pete and Schramm (2013).

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BibTeX RIS

Gábor Pete. 2015-07-16. The tail of the crossing probability in near-critical percolation --- an appendix to Ahlberg & Steif [arXiv:1405.7144]. https://arxiv.org/abs/1507.05522

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