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First critical probability for a problem on random orientations in $G(n,p)$.


 
Dublin Core PKP Metadata Items Metadata for this Document
 
1. Title Title of document First critical probability for a problem on random orientations in $G(n,p)$.
 
2. Creator Author's name, affiliation, country Sven Erick Alm; Uppsala Universitet; Sweden
 
2. Creator Author's name, affiliation, country Svante Janson; Uppsala Universitet; Sweden
 
2. Creator Author's name, affiliation, country Svante Linusson; KTH- Royal Institute of Technology; Sweden
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Random directed graph, correlation, directed paths
 
3. Subject Subject classification 05C80, 05C20, 05C38, 60C05
 
4. Description Abstract 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 $\{a\to s\}$ (there exists a directed path from $a$ to $s$) and $\{s\to b\}$. We prove that asymptotically the correlation is negative for small $p$, $p<\frac{C_1}n$, where $C_1\approx0.3617$, positive for $\frac{C_1}n<p<\frac2n$ and up to $p=p_2(n)$. Computer aided computations suggest that $p_2(n)=\frac{C_2}n$, with $C_2\approx7.5$. We conjecture that the correlation  then stays negative for $p$ up to the previously known zero at $\frac12$; for larger $p$ it is positive.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) Knut and Alice Wallenberg Foundation
 
7. Date (YYYY-MM-DD) 2014-08-14
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/2725
 
10. Identifier Digital Object Identifier 10.1214/EJP.v19-2725
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 19
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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