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First critical probability for a problem on random orientations in G(n,p)
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0001-6339-2230
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
URN: urn:nbn:se:kth:diva-152584DOI: 10.1214/EJP.v19-2725ISI: 000341101500001ScopusID: 2-s2.0-84907333471OAI: diva2:750530
Knut and Alice Wallenberg Foundation

QC 20140929

Available from: 2014-09-29 Created: 2014-09-29 Last updated: 2014-09-29Bibliographically approved

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Linusson, Svante
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