The number of components in a logarithmic combinatorial structure
Arratia, Richard ; Barbour, A. D. ; Tavaré, Simon
Ann. Appl. Probab., Tome 10 (2000) no. 2, p. 331-361 / Harvested from Project Euclid
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Under very mild conditions, we prove that the number of components in a decomposable logarithmic combinatorial structure has a distribution which is close to Poisson in total variation. The conditions are satisfied for all assemblies, multisets and selections in the logarithmic class.The error in the Poisson approximation is shown under marginally more restrictive conditions to be of exact order $O(1/\log n)$, by exhibiting the penultimate asymptotic approximation; similar results have previously been obtained by Hwang [20], under stronger assumptions.Our method is entirely probabilistic, and the conditions can readily be verified in practice.
Publié le : 2000-05-14
Classification:  Logarithmic combinatorial structures,  component counts,  total variation approximation,  Poisson approximation,  60C05,  60F05,  05A16 
@article{1019487347,
     author = {Arratia, Richard and Barbour, A. D. and Tavar\'e, Simon},
     title = {The number of components in a logarithmic combinatorial
		 structure},
     journal = {Ann. Appl. Probab.},
     volume = {10},
     number = {2},
     year = {2000},
     pages = { 331-361},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1019487347}
}

Arratia, Richard; Barbour, A. D.; Tavaré, Simon. The number of components in a logarithmic combinatorial
		 structure. Ann. Appl. Probab., Tome 10 (2000) no. 2, pp.  331-361. http://gdmltest.u-ga.fr/item/1019487347/