Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-22060
Arratia, R; Barbour, A D; Tavaré, S (2000). The number of components in a logarithmic combinatorial structure. Annals of Applied Probability, 10(2):331-361.
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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 , under stronger assumptions.Our method is entirely probabilistic, and the conditions can readily be verified in practice.
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|Item Type:||Journal Article, refereed, original work|
|Communities & Collections:||07 Faculty of Science > Institute of Mathematics|
|Dewey Decimal Classification:||510 Mathematics|
|Uncontrolled Keywords:||Logarithmic combinatorial structures; component counts; total variation approximation; Poisson approximation|
|Deposited On:||07 Apr 2010 12:39|
|Last Modified:||23 Nov 2012 13:26|
|Publisher:||Institute of Mathematical Statistics|
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