Change search
ReferencesLink to record
Permanent link

Direct link
Correlations for Paths in Random Orientations of G(n, p) and G(n, m)
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0001-6339-2230
2011 (English)In: Random structures & algorithms (Print), ISSN 1042-9832, E-ISSN 1098-2418, Vol. 39, no 4, 486-506 p.Article in journal (Refereed) Published
Abstract [en]

We study random graphs, both G(n, p) and G(n, m), with random orientations on the edges. For three fixed distinct vertices s, a, b we study the correlation, in the combined probability space, of the events {a -> s} and {s -> b}. For G(n, p), we prove that there is a p(c) = 1/2 such that for a fixed p < p(c) the correlation is negative for large enough n and for p > p(c) the correlation is positive for large enough n. We conjecture that for a fixed n >= 27 the correlation changes sign three times for three critical values of p. For G(n, m) it is similarly proved that, with p = m/((n)(2)), there is a critical p(c) that is the solution to a certain equation and approximately equal to 0.7993. A lemma, which computes the probability of non existence of any l directed edges in G(n, m), is thought to be of independent interest. We present exact recursions to compute P(a -> s) and P(a -> s, s -> b). We also briefly discuss the corresponding question in the quenched version of the problem.

Place, publisher, year, edition, pages
2011. Vol. 39, no 4, 486-506 p.
Keyword [en]
random directed graphs, correlation, directed paths, annealed, quenched
National Category
URN: urn:nbn:se:kth:diva-51413DOI: 10.1002/rsa.20358ISI: 000296716500002ScopusID: 2-s2.0-80054838779OAI: diva2:464535
Knut and Alice Wallenberg Foundation
QC 20111213Available from: 2011-12-13 Created: 2011-12-12 Last updated: 2011-12-13Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full textScopus

Search in DiVA

By author/editor
Linusson, Svante
By organisation
Mathematics (Div.)
In the same journal
Random structures & algorithms (Print)

Search outside of DiVA

GoogleGoogle Scholar
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

Altmetric score

Total: 25 hits
ReferencesLink to record
Permanent link

Direct link