Large‐deviations/thermodynamic approach to percolation on the complete graph

DOI10.1002/rsa.20169zbMath1129.05045arXivmath/0506255OpenAlexW2950173676MaRDI QIDQ5433266

S. Alex Smith, Marek Biskup, Lincoln Chayes

Publication date: 8 January 2008

Published in: Random Structures & Algorithms (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0506255

zbMATH Keywords

percolationlarge deviationsrandom forestsErdős-Renyi random graph

Mathematics Subject Classification ID

Random graphs (graph-theoretic aspects) (05C80) Combinatorial probability (60C05)

Related Items (10)

Partition Functions of Discrete Coalescents: From Cayley’s Formula to Frieze’s ζ(3) Limit Theorem ⋮ Large deviation analysis for layered percolation problems on the complete graph ⋮ Limit theorems and coexistence probabilities for the Curie-Weiss Potts model with an external field ⋮ Large-deviation properties of largest component for random graphs ⋮ Exploring hypergraphs with martingales ⋮ The cut metric, random graphs, and branching processes ⋮ Large deviations of empirical neighborhood distribution in sparse random graphs ⋮ Asymptotic distribution of the numbers of vertices and arcs of the giant strong component in sparse random digraphs ⋮ The random cluster model on the complete graph via large deviations ⋮ Large deviation theory of percolation on multiplex networks

Cites Work

• Rigorous analysis of discontinuous phase transitions via mean-field bounds
• Critical region for droplet formation in the two-dimensional Ising model
• Percolation
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