TY - JOUR
T1 - Asymptotic normality determined by high moments, and submap counts of random maps
AU - Gao, Zhicheng
AU - Wormald, Nicholas C.
PY - 2004/11
Y1 - 2004/11
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=8744253702&partnerID=8YFLogxK
U2 - 10.1007/s00440-004-0356-9
DO - 10.1007/s00440-004-0356-9
M3 - Article
AN - SCOPUS:8744253702
VL - 130
SP - 368
EP - 376
JO - Probability Theory and Related Fields
JF - Probability Theory and Related Fields
SN - 0178-8051
IS - 3
ER -