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

Zhicheng Gao, Nicholas C. Wormald

Research output: Contribution to journalArticleResearchpeer-review

16 Citations (Scopus)


We give a general result showing that the asymptotic behaviour of high moments determines the shape of distributions which are asymptotically normal. Both the factorial and non-factorial (non-central) moments are treated. This differs from the usual moment method in combinatorics, as the expected value may tend to infinity quite rapidly. Applications are given to submap counts in random planar triangulations, where we use a simple argument to asymptotically determine high moments for the number of copies of a given subtriangulation in a random 3-connected planar triangulation. Similar results are also obtained for 2-connected triangulations and quadrangulations with no multiple edges.

Original languageEnglish
Pages (from-to)368-376
Number of pages9
JournalProbability Theory and Related Fields
Issue number3
Publication statusPublished - Nov 2004
Externally publishedYes

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