On the continuity of the critical value for long range percolation in the exponential case

DOI10.1007/BF02099722zbMath0878.60068OpenAlexW1978849526MaRDI QIDQ1357417

Jeffrey E. Steif, Ronald W. J. Meester

Publication date: 10 June 1997

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02099722

zbMATH Keywords

critical valuessupercritical regimeexponentially decaying connectionslong range percolation models

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Percolation (82B43)

Related Items (10)

Truncated long-range percolation on oriented graphs ⋮ Supercritical loop percolation on \(\mathbb{Z}^d\) for \(d \geq 3\) ⋮ A note on truncated long-range percolation with heavy tails on oriented graphs ⋮ The diameter of long-range percolation clusters on finite cycles ⋮ Truncation of long-range percolation model with square non-summable interactions ⋮ On the truncation of systems with non-summable interactions ⋮ Slab percolation for the Ising model ⋮ On the Truncated Long-Range Percolation on Z² ⋮ Long-range contact process and percolation on a random lattice ⋮ On the truncated anisotropic long-range percolation on \(\mathbb Z^2\)

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• Discontinuity of the percolation density in one dimensional \(1/| x- y| ^ 2\) percolation models
• On the continuity of the percolation probability function
• The supercritical phase of percolation is well behaved

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