<div class="csl-bib-body">
<div class="csl-entry">van Engelenburg, D. G. P., Garban, C., Panis, R., & Severo, F. (2025). <i>One-arm exponents of high-dimensional percolation revisited</i>. arXiv. https://doi.org/10.48550/arXiv.2510.21595</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/224746
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dc.description.abstract
We consider sufficiently spread-out Bernoulli percolation in dimensions đť‘‘ > 6. We present a short and simple proof of the up-to-constants estimate for the one-arm probability in both the full-space and half-space settings. These results were previously established by Kozma and Nachmias and by Chatterjee and Hanson, respectively. Our proof improves upon the entropic technique introduced by Dewan and Muirhead, relying on a sharp estimate on a suitably chosen correlation length recently obtained by Duminil-Copin and Panis. This approach is inspired by our companion work, where we compute the one-arm exponent for several percolation models related to the high-dimensional Ising model.
en
dc.language.iso
en
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dc.subject
Percolation
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dc.subject
Bernoulli Percolation
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dc.subject
High Dimensions
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dc.subject
Arm Exponent
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dc.title
One-arm exponents of high-dimensional percolation revisited
