Edge percolation on a random regular graph of low degree

DOI10.1214/07-AOP361zbMath1160.05054arXiv0808.3516OpenAlexW3103182906MaRDI QIDQ941299

Boris G. Pittel

Publication date: 4 September 2008

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

Full work available at URL: https://arxiv.org/abs/0808.3516

zbMATH Keywords

Random graphPercolationGiant componentThreshold probabilityTransition window

Mathematics Subject Classification ID

Martingales with discrete parameter (60G42) Random graphs (graph-theoretic aspects) (05C80) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics (82C20) Critical phenomena in equilibrium statistical mechanics (82B27)

Related Items

Mean-field conditions for percolation on finite graphs ⋮ Locality of random digraphs on expanders ⋮ Giant vacant component left by a random walk in a random \(d\)-regular graph ⋮ Asymptotics in percolation on high‐girth expanders ⋮ Expansion properties of a random regular graph after random vertex deletions ⋮ Sharp threshold for percolation on expanders ⋮ The Evolution of the Cover Time ⋮ On the largest component of a random graph with a subpower-law degree sequence in a subcritical phase ⋮ The sharp threshold for percolation on expander graphs ⋮ Critical percolation on random regular graphs ⋮ On a random graph evolving by degrees ⋮ Critical window for the vacant set left by random walk on random regular graphs ⋮ An old approach to the giant component problem ⋮ Percolation on Random Graphs with a Fixed Degree Sequence ⋮ Critical percolation on random regular graphs

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A probabilistic proof of an asymptotic formula for the number of labelled regular graphs
• The asymptotic number of labeled graphs with given degree sequences
• On the largest component of the random graph at a nearcritical stage
• Percolation on finite graphs and isoperimetric inequalities.
• Differential equations for random processes and random graphs
• Sudden emergence of a giant \(k\)-core in a random graph
• Random subgraphs of finite graphs. II: The lace expansion and the triangle condition
• Some general results concerning the critical exponents of percolation processes
• Bootstrap percolation on the random regular graph
• The Evolution of Random Graphs
• Component behavior near the critical point of the random graph process
• On the number of sparse connected graphs
• The Size of the Giant Component of a Random Graph with a Given Degree Sequence
• The Structure of a Random Graph at the Point of the Phase Transition
• On a random graph with immigrating vertices: Emergence of the giant component
• A critical point for random graphs with a given degree sequence
• The Asymptotic Number of Unlabelled Regular Graphs
• The birth of the giant component
• Random subgraphs of finite graphs: I. The scaling window under the triangle condition