Published August 25, 2020
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Power-law bounds for critical long-range percolation below the upper-critical dimension
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Abstract
We study long-range Bernoulli percolation on ℤd in which each two vertices x and y are connected by an edge with probability 1−exp(−β‖x−y‖−d−α). It is a theorem of Noam Berger (CMP, 2002) that if 0<α
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Dedicated to Harry Kesten, November 19, 1931 - March 29, 2019. We thank Jonathan Hermon for his careful reading of an earlier version of this manuscript, and thank Gordon Slade for helpful discussions on the physics literature. We also thank the anonymous referee for their helpful comments and corrections.Attached Files
Accepted Version - 2008.11197.pdf
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2008.11197.pdf
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- Eprint ID
- 111034
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- CaltechAUTHORS:20210924-202126385
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- Describes
- http://arxiv.org/abs/2008.11197 (URL)
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2021-09-27Created from EPrint's datestamp field
- Updated
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2023-06-02Created from EPrint's last_modified field
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