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2009

A note on correlations in randomly oriented graphs

Linusson, Svante

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Given a graph $G$, we consider the model where $G$ is given a random orientation by giving each edge a random direction.

It is proven that for $a,b,s\in V(G)$, the events $\{s\to a\}$ and $\{s\to b\}$ are positively correlated.
This correlation persists, perhaps unexpectedly, also if we first condition on $\{s\nto t\}$ for any vertex $t\neq s$.
With this conditioning it is also true that $\{s\to b\}$ and $\{a\to t\}$ are negatively correlated.

A note on correlations in randomly oriented graphs · Around

Built on

Theodore E. Harris, A lower bound for the critical probability in a certain percolation process. Proc. Cambridge Philos. Soc
1960
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Colin Mc Diarmid, General Percolation and random Adv. Appl. Prob
1981
Earlier work this paper cites.
Eric Babson, Anders Björner, Svante Linusson, John Shareshian, and Volkmar Welker, Complexes of not i i -connected graphs
1999
Earlier work this paper cites.
Geoffrey R. Grimmett, Percolation
1999
Earlier work this paper cites.

Similar

Jacob van den Berg and Jeff Kahn, A correlation inequality for connection events in percolation, Annals of Probability
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Jacob van den Berg, Olle Häggström and Jeff Kahn, Some conditional correlation inequalities for percolation on related prcesses, Rand. Structures Algorithms
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Then

Jakob Jonsson, Simplicial Complexes of Graphs
2008
Later among the works it cites.
Svante Linusson, On percolation and the bunkbed conjecture, Preprint 2008
Original
2008
Later among the works it cites.
Sven Erick Alm and Svante Linusson, A counter-intuitive correlation in a random tournament, Preprint 2009
2009
Closest in time.
Sven Erick Alm and Svante Linusson, Correlations for paths in random orientations of G ⁡ ( n , p ) G(n,p) , Preprint 2009
2009
Closest in time.

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