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First critical probability for a problem on random orientations in G(n,p)
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).ORCID-id: 0000-0001-6339-2230
2014 (engelsk)Inngår i: Electronic Journal of Probability, ISSN 1083-6489, E-ISSN 1083-6489, Vol. 19, s. 69-Artikkel i tidsskrift (Fagfellevurdert) 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.

sted, utgiver, år, opplag, sider
2014. Vol. 19, s. 69-
Emneord [en]
random directed graphs, correlation, directed paths
HSV kategori
Identifikatorer
URN: urn:nbn:se:kth:diva-152584DOI: 10.1214/EJP.v19-2725ISI: 000341101500001Scopus ID: 2-s2.0-84907333471OAI: oai:DiVA.org:kth-152584DiVA, id: diva2:750530
Forskningsfinansiär
Knut and Alice Wallenberg Foundation
Merknad

QC 20140929

Tilgjengelig fra: 2014-09-29 Laget: 2014-09-29 Sist oppdatert: 2017-12-05bibliografisk kontrollert

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Totalt: 249 treff
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