The variance of the graph distance in the infinite cluster of percolation is sublinear
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Date
2024
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Journal Article
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yes
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Abstract
We consider the standard model of i.i.d. bond percolation on Zᵈ of parameter p. When p > p꜀ where p꜀ denotes the critical parameter, there exists almost surely a unique infinite cluster C∞. Using the recent techniques of Cerf and Dembin (2022), we prove that the variance of the graph distance in C∞ between two points of C∞ is sublinear. This result extends the works of Benjamini et al. (2003), Benaïm and Rossignol (2008) and Damron et al. (2015) for the study of the variance of passage times in first passage percolation without moment conditions on the edge-weight
distribution.
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published
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21
Pages / Article No.
307 - 320
Publisher
Institute of Mathematical Statistics
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Subject
Percolation; chemical distance; concentration
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Funding
175505 - Loops, paths and fields (SNF)