Critical values in a long-range percolation on spaces like fractals

DOI10.1007/S10955-006-9243-3zbMath1114.82015OpenAlexW2027427977MaRDI QIDQ867705

Jun Misumi

Publication date: 16 February 2007

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10955-006-9243-3

zbMATH Keywords

phase transitionfractalsLong-range percolation

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Phase transitions (general) in equilibrium statistical mechanics (82B26) Percolation (82B43)

Related Items (1)

The diameter of a long-range percolation cluster on pre-Sierpinski gasket

Cites Work

• One dimensional \(1/| j-i| ^ s\) percolation models: The existence of a transition for s\(\leq 2\)
• When are random graphs connected
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• On the scaling of the chemical distance in long-range percolation models
• 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
• On the chemical distance for supercritical Bernoulli percolation
• The diameter of long-range percolation clusters on finite cycles
• Existence of phase transition of percolation on Sierpiński carpet lattices
• The diameter of a long-range percolation graph
• On the connectedness of a random graph

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