Couplings for Irregular Combinatorial Assemblies

  • Andrew BarbourEmail author
  • Anna Pósfai
Conference paper
Part of the Lecture Notes in Statistics book series (LNS, volume 205)


When approximating the joint distribution of the component counts of a decomposable combinatorial structure that is ‘almost’ in the logarithmic class, but nonetheless has irregular structure, it is useful to be able first to establish that the distribution of a certain sum of non-negative integer valued random variables is smooth. This distribution is not like the normal, and individual summands can contribute a non-trivial amount to the whole, so its smoothness is somewhat surprising. In this paper, we consider two coupling approaches to establishing the smoothness, and contrast the results that are obtained.


Failure Probability Independent Random Variable Probability Mass Function Coupling Approach Total Variation Distance 
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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Angewandte MathematikUniversität ZürichZürichSwitzerland
  2. 2.Department of MathematicsTufts UniversityMedfordUSA
  3. 3.Analysis and Stochastics Research Group of the Hungarian Academy of Sciences, Bolyai InstituteUniversity of SzegedSzegedHungary

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