On the critical probability in percolation

DOI10.1214/17-EJP52zbMath1387.05239arXiv1611.08549MaRDI QIDQ1748902

Lutz Warnke, Svante Janson

Publication date: 15 May 2018

Published in: Electronic Journal of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.08549

zbMATH Keywords

percolationphase transitioncritical probabilityrandom graphcritical window

Mathematics Subject Classification ID

Random graphs (graph-theoretic aspects) (05C80) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Combinatorial probability (60C05) Percolation (82B43)

Related Items

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Uses Software

• DLMF

Cites Work

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• Hypercube percolation
• A note about critical percolation on finite graphs
• Random subgraphs of finite graphs. III: The phase transition for the \(n\)-cube
• Critical random graphs: Diameter and mixing time
• Brownian excursion area, wright's constants in graph enumeration, and other Brownian areas
• The Alexander-Orbach conjecture holds in high dimensions
• Tail estimates for the Brownian excursion area and other Brownian areas
• The Brownian excursion area: A numerical analysis
• Tree graph inequalities and critical behavior in percolation models
• Largest random component of a k-cube
• Brownian excursions, critical random graphs and the multiplicative coalescent
• Random subgraphs of the 2D Hamming graph: The supercritical phase
• Unlacing hypercube percolation: a survey
• Random subgraphs of finite graphs. II: The lace expansion and the triangle condition
• A power law of order 1/4 for critical mean-field Swendsen-Wang dynamics
• The evolution of subcritical Achlioptas processes
• On the strength of connectedness of a random graph
• Expansion in ${\boldsymbol{n^{-1}}}$ for Percolation Critical Values on the $n$-cube and ${\boldsymbol{{\mathbb Z}^n}}$: the First Three Terms
• Susceptibility in subcritical random graphs
• The Evolution of Random Graphs
• On the critical percolation probabilities
• Component behavior near the critical point of the random graph process
• The Evolution of Random Subgraphs of the Cube
• The number of connected sparsely edged graphs
• Percolation
• Enumerating graphs and Brownian motion
• Probability: A Graduate Course
• Random subgraphs of finite graphs: I. The scaling window under the triangle condition
• A Point Process Describing the Component Sizes in the Critical Window of the Random Graph Evolution
• The total progeny in a branching process and a related random walk
• Exploring hypergraphs with martingales