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First critical probability for a problem on random orientations in G(n,p)
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2014 (English)In: Electronic Journal of Probability, ISSN 1083-6489, Vol. 19, 69- p.Article in journal (Refereed) Published
Abstract [en]

We study the random graph G (n,p) with a random orientation. For three fixed vertices s, a, b in G(n,p) we study the correlation of the events {a -> s} (there exists a directed path from a to s) and {s -> b}. We prove that asymptotically the correlation is negative for small p, p < C-1/n, where C-1 approximate to 0.3617, positive for C-1/n < p < 2/n and up to p = p(2)(n). Computer aided computations suggest that p(2)(n) = C-2/n, with C-2 approximate to 7.5. We conjecture that the correlation then stays negative for p up to the previously known zero at 1/2; for larger p it is positive.

Place, publisher, year, edition, pages
2014. Vol. 19, 69- p.
Keyword [en]
random directed graphs, correlation, directed paths
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:uu:diva-233025DOI: 10.1214/EJP.v19-2725ISI: 000341101500001OAI: oai:DiVA.org:uu-233025DiVA: diva2:751029
Available from: 2014-09-30 Created: 2014-09-29 Last updated: 2014-09-30Bibliographically approved

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Alm, Sven ErickJanson, Svante
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