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
Convergence to the Tracy-Widom distribution for longest paths in a directed random graph
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2013 (English)In: Latin American Journal of Probability and Mathematical Statistics, ISSN 1980-0436, E-ISSN 1980-0436, Vol. 10, no 2, p. 711-730Article in journal (Refereed) Published
Abstract [en]

We consider a directed graph on the 2-dimensional integer lattice, placing a directed edge from vertex (i(1), i(2)) to (j(1), j(2)), whenever i(1) <= j(1), i(2) <= j(2), with probability p, independently for each such pair of vertices. Let L-n,L-m denote the maximum length of all paths contained in an n x m rectangle. We show that there is a positive exponent a, such that, if m/n(a) -> 1, as n -> infinity, then a properly centered/rescaled version of L-n,L-m converges weakly to the Tracy-Widom distribution. A generalization to graphs with non-constant probabilities is also discussed.

Place, publisher, year, edition, pages
2013. Vol. 10, no 2, p. 711-730
Keyword [en]
Random graph, last passage percolation, strong approximation, Tracy-Widom distribution
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-309908ISI: 000346351400009OAI: oai:DiVA.org:uu-309908DiVA, id: diva2:1056701
Available from: 2016-12-15 Created: 2016-12-08 Last updated: 2017-11-29Bibliographically approved

Open Access in DiVA

fulltext(504 kB)33 downloads
File information
File name FULLTEXT01.pdfFile size 504 kBChecksum SHA-512
8281f14250c179e93e596ef4c3774100f9e8888caf84b198a4534ee347fed47738727abf158ecff5b1f3762c8190163c5f80dacf18cdb16c033f6129ea38c6d2
Type fulltextMimetype application/pdf

Other links

fulltextArXiv

Search in DiVA

By author/editor
Konstantopoulos, TakisGabrysch, Katja
By organisation
Analysis and Probability Theory
In the same journal
Latin American Journal of Probability and Mathematical Statistics
Mathematics

Search outside of DiVA

GoogleGoogle Scholar
Total: 33 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

urn-nbn

Altmetric score

urn-nbn
Total: 494 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