Asymptotic normality determined by high moments, and submap counts of random maps
成果类型：
Article
署名作者：
Gao, ZC; Wormald, NC
署名单位：
University of Macau; University of Waterloo; University of Melbourne
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-004-0356-9
发表日期：
2004
页码：
368-376
关键词：
摘要：
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.
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