Asymptotic normality determined by high moments, and submap counts of random maps

DOI10.1007/s00440-004-0356-9zbMath1058.60015OpenAlexW1987172896MaRDI QIDQ1765109

Nicholas C. Wormald, Zhi-Cheng Gao

Publication date: 22 February 2005

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00440-004-0356-9

zbMATH Keywords

quadrangulationsrandom planar triangulations2-connected triangulations3-connected planar triangulation

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Central limit and other weak theorems (60F05) Probability distributions: general theory (60E05) Combinatorics on words (68R15) Graph theory (including graph drawing) in computer science (68R10) Probabilistic methods in extremal combinatorics, including polynomial methods (combinatorial Nullstellensatz, etc.) (05D40)

Related Items (12)

Testing community structure for hypergraphs ⋮ Triangles in random cubic planar graphs ⋮ A central limit theorem for the number of degree-\(k\) vertices in random maps ⋮ Unnamed Item ⋮ Triangles and subgraph probabilities in random regular graphs ⋮ A study of large fringe and non-fringe subtrees in conditional Galton-Watson trees ⋮ On properties of random dissections and triangulations ⋮ Random graphs on surfaces ⋮ The bivariate Ising polynomial of a graph ⋮ A probabilistic approach to value sets of polynomials over finite fields ⋮ Pattern occurrences in random planar maps ⋮ Distribution of the number of spanning regular subgraphs in random graphs

Cites Work

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• Sharp concentration of the number of submaps in random planar triangulations
• Random triangulations of the plane
• Submaps of maps. I: General 0-1 laws
• On pattern frequency occurrences in a Markovian sequence
• Almost all maps are asymmetric
• The random bipartite nearest neighbor graphs
• Enumeration of Quadrangular Dissections of the Disk

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