uu.seUppsala University Publications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Sub-Gaussian tail bounds for the width and height of conditioned Galton–Watson trees
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2013 (English)In: Annals of Probability, ISSN 0091-1798, E-ISSN 2168-894X, Vol. 41, no 2, 1072-1087 p.Article in journal (Refereed) Published
Abstract [en]

We study the height and width of a Galton-Watson tree with offspring distribution xi satisfying E xi = 1, 0 < Var xi < infinity, conditioned on having exactly n nodes. Under this conditioning, we derive sub-Gaussian tail bounds for both the width (largest number of nodes in any level) and height (greatest level containing a node); the bounds are optimal up to constant factors in the exponent. Under the same conditioning, we also derive essentially optimal upper tail bounds for the number of nodes at level k, for 1 <= k <= n.

Place, publisher, year, edition, pages
2013. Vol. 41, no 2, 1072-1087 p.
Keyword [en]
Random trees, Galton-Watson trees, simply generated trees, width, height
National Category
Natural Sciences
Identifiers
URN: urn:nbn:se:uu:diva-199732DOI: 10.1214/12-AOP758ISI: 000317157300019OAI: oai:DiVA.org:uu-199732DiVA: diva2:621029
Available from: 2013-05-13 Created: 2013-05-13 Last updated: 2017-12-06Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full text

Authority records BETA

Janson, Svante

Search in DiVA

By author/editor
Janson, Svante
By organisation
Department of Mathematics
In the same journal
Annals of Probability
Natural Sciences

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 363 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf