Continuum percolation and Euclidean minimal spanning trees in high dimensions

DOI10.1214/aoap/1034968142zbMath0855.60096OpenAlexW2046268301MaRDI QIDQ1814749

Mathew D. Penrose

Publication date: 14 January 1997

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

Full work available at URL: https://doi.org/10.1214/aoap/1034968142

zbMATH Keywords

phase transitionsbranching processPoisson processcontinuum percolationhigh dimensionsgeometric probabilityminimal spanning tree constant

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Percolation (82B43) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Related Items (17)

Nonoptimality of constant radii in high dimensional continuum percolation ⋮ Continuum percolation in high dimensions ⋮ Sharpness of the phase transition and lower bounds for the critical intensity in continuum percolation on \(\mathbb{R}^{d}\) ⋮ The threshold contact process: A continuum limit ⋮ The random connection model in high dimensions ⋮ Percolation for the stable marriage of Poisson and Lebesgue ⋮ An explicit Dobrushin uniqueness region for Gibbs point processes with repulsive interactions ⋮ On the uniqueness of Gibbs distributions with a non-negative and subcritical pair potential ⋮ Percolation in the Boolean model with convex grains in high dimension ⋮ Phase transition in a stochastic geometry model with applications to statistical mechanics ⋮ Automatic choice of the threshold of a grain filter via Galton-Watson trees: application to granite cracks detection ⋮ Percolation on fitness landscapes: effects of correlation, phenotype, and incompatibilities ⋮ Percolation in the secrecy graph ⋮ Decorrelation of a class of Gibbs particle processes and asymptotic properties of U-statistics ⋮ The random minimal spanning tree in high dimensions ⋮ Disagreement percolation for the hard-sphere model ⋮ Giant component of the soft random geometric graph

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An asymptotic determination of the minimum spanning tree and minimum matching constants in geometrical probability
• An upper bound on the critical percolation probability for the three- dimensional cubic lattice
• Growth rates of Euclidean minimal spanning trees with power weighted edges
• The minimum spanning tree constant in geometrical probability and under the independent model: A unified approach
• Asymptotics for Euclidean minimal spanning trees on random points
• On the spread-out limit for bond and continuum percolation
• Finite clusters in high-density continuous percolation: Compression and sphericality
• The random connection model in high dimensions
• Single linkage clustering and continuum percolation
• On a continuum percolation model
• Nearest neighbor and hard sphere models in continuum percolation
• The total progeny in a branching process and a related random walk

This page was built for publication: Continuum percolation and Euclidean minimal spanning trees in high dimensions