Correlations for paths in random orientations of G (n, p) and G (n, m)

S Erick Alm, S Janson… - Random Structures & …, 2011 - Wiley Online Library
Abstract 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 combine
probability space, of the events {a→s\} and {s→b\}. For G (n, p), we prove that there is a
pc=1/2 such that for a fixed p<pc the correlation is negative for large enough n and for p>pc
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 …

[PDF][PDF] Correlations for paths in random orientations of G (n, p)

SE Alm, S Linusson - Preprint, 2009 - Citeseer
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} and {s→ b}. We prove that for a fixed
p< 1/2 the correlation is negative for large enough n and for p> 1/2 the correlation is positive
for large enough n. We present exact recursions to compute P (a→ s) and P (a→ s, s→ b).
We conjecture that for a fixed n≥ 27 the correlation changes sign three times for three
critical values of p.
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