Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • 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
On percolation in one-dimensional stable Poisson graphs
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2015 (English)In: Electronic Communications in Probability, ISSN 1083-589X, E-ISSN 1083-589X, Vol. 20Article in journal (Refereed) Published
Abstract [en]

Equip each point x of a homogeneous Poisson point process P on R with D-x edge stubs, where the D-x are i.i.d. positive integer-valued random variables with distribution given by mu. Following the stable multi-matching scheme introduced by Deijfen, Haggstrom and Holroyd [1], we pair off edge stubs in a series of rounds to form the edge set of a graph G on the vertex set P. In this note, we answer questions of Deijfen, Holroyd and Peres [2] and Deijfen, Haggstrom and Holroyd [1] on percolation (the existence of an infinite connected component) in G. We prove that percolation may occur a.s. even if mu has support over odd integers. Furthermore, we show that for any epsilon > 0, there exists a distribution mu such that mu ({1}) > 1 - epsilon, but percolation still occurs a.s..

Place, publisher, year, edition, pages
2015. Vol. 20
Keyword [en]
Poisson process, Random graph, Matching, Percolation
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-258752DOI: 10.1214/ECP.v20-3958ISI: 000357151400001OAI: oai:DiVA.org:uu-258752DiVA: diva2:842544
Funder
Swedish Research Council
Available from: 2015-07-21 Created: 2015-07-20 Last updated: 2017-12-04Bibliographically approved

Open Access in DiVA

fulltext(191 kB)124 downloads
File information
File name FULLTEXT01.pdfFile size 191 kBChecksum SHA-512
d3b234a05d164166f2cec93d0235aef6fc26ceca95bf9a1c3d79f6b2ceb87b8842f34755f0647e121cb1e24dd1140cc1bd098808ab0435f8c4874ddc52a7d66e
Type fulltextMimetype application/pdf

Other links

Publisher's full text

Search in DiVA

By author/editor
Björklund, JohanHolmgren, Cecilia
By organisation
Algebra and GeometryAnalysis and Probability Theory
In the same journal
Electronic Communications in Probability
Mathematics

Search outside of DiVA

GoogleGoogle Scholar
Total: 124 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 569 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • 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