Graph distances of continuum long-range percolation

DOI10.1214/21-BJPS500MaRDI QIDQ2244849

Ercan Sönmez

Publication date: 12 November 2021

Published in: Brazilian Journal of Probability and Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.10933

zbMATH Keywords

random graphsdiameterPoisson processgraph distancerandom connection modellong-range percolation

Mathematics Subject Classification ID

Combinatorics (05-XX) Statistical mechanics, structure of matter (82-XX)

Related Items (1)

Random walk on the random connection model

Cites Work

• Scale-free percolation
• One dimensional \(1/| j-i| ^ s\) percolation models: The existence of a transition for s\(\leq 2\)
• Geometry of the uniform spanning forest: transitions in dimensions 4, 8, 12,\dots
• Discontinuity of the percolation density in one dimensional \(1/| x- y| ^ 2\) percolation models
• Scale-free percolation in continuum space
• The diameter of long-range percolation clusters on finite cycles
• The diameter of a long-range percolation graph
• On a continuum percolation model
• Sharp asymptotic for the chemical distance in long‐range percolation
• Collective dynamics of ‘small-world’ networks

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