License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.AofA.2018.33
URN: urn:nbn:de:0030-drops-89262
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/8926/
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Ralaivaosaona, Dimbinaina ; Sileikis, Matas ; Wagner, Stephan

Asymptotic Normality of Almost Local Functionals in Conditioned Galton-Watson Trees

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Abstract

An additive functional of a rooted tree is a functional that can be calculated recursively as the sum of the values of the functional over the branches, plus a certain toll function. Janson recently proved a central limit theorem for additive functionals of conditioned Galton-Watson trees under the assumption that the toll function is local, i.e. only depends on a fixed neighbourhood of the root. We extend his result to functionals that are almost local, thus covering a wider range of functionals. Our main result is illustrated by two explicit examples: the (logarithm of) the number of matchings, and a functional stemming from a tree reduction process that was studied by Hackl, Heuberger, Kropf, and Prodinger.

BibTeX - Entry

@InProceedings{ralaivaosaona_et_al:LIPIcs:2018:8926,
  author =	{Dimbinaina Ralaivaosaona and Matas Sileikis and Stephan Wagner},
  title =	{{Asymptotic Normality of Almost Local Functionals in Conditioned Galton-Watson Trees}},
  booktitle =	{29th International Conference on Probabilistic,  Combinatorial and Asymptotic Methods for the Analysis of Algorithms  (AofA 2018)},
  pages =	{33:1--33:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-078-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{110},
  editor =	{James Allen Fill and Mark Daniel Ward},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8926},
  URN =		{urn:nbn:de:0030-drops-89262},
  doi =		{10.4230/LIPIcs.AofA.2018.33},
  annote =	{Keywords: Galton-Watson trees, central limit theorem, additive functional}
}

Keywords: Galton-Watson trees, central limit theorem, additive functional
Collection: 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018)
Issue Date: 2018
Date of publication: 18.06.2018

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