On the spread-out limit for bond and continuum percolation

DOI10.1214/aoap/1177005518zbMath0771.60097OpenAlexW1965887892MaRDI QIDQ1210495

Mathew D. Penrose

Publication date: 4 October 1993

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aoap/1177005518

zbMATH Keywords

critical probabilitymean-field limitGalton-Watson processBernoulli bond percolationpercolation models

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Percolation (82B43) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Related Items (16)

Site and bond percolation on four-dimensional simple hypercubic lattices with extended neighborhoods ⋮ Self-avoiding walks and trees in spread-out lattices ⋮ The threshold contact process: A continuum limit ⋮ The random connection model in high dimensions ⋮ An upper bound for \(p_c\) in range-\(R\) bond percolation in two and three dimensions ⋮ The direct-connectedness function in the random connection model ⋮ Strict inequalities of critical values in continuum percolation ⋮ Connected spatial networks over random points and a route-length statistic ⋮ Effect of scale on long-range random graphs and chromosomal inversions ⋮ Line-of-Sight Percolation ⋮ The random minimal spanning tree in high dimensions ⋮ Some remarks on AB-percolation in high dimensions ⋮ Continuum percolation with unreliable and spread-out connections ⋮ Phase transition in random distance graphs on the torus ⋮ The disk-percolation model on graphs ⋮ Continuum percolation and Euclidean minimal spanning trees in high dimensions

This page was built for publication: On the spread-out limit for bond and continuum percolation