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Phase-transition-like phenomenon in a piecewise linear map

✍ Scribed by R. Kluiving; H.W. Capel; R.A. Pasmanter


Book ID
108004206
Publisher
Elsevier Science
Year
1990
Tongue
English
Weight
850 KB
Volume
164
Category
Article
ISSN
0378-4371

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Let a random directed acyclic graph be defined as being obtained from the random graph G n p by orienting the edges according to the ordering of vertices. Let Ξ³ \* n be the size of the largest (reflexive, transitive) closure of a vertex. For p = c log n /n, we prove that, with high probability, Ξ³ \*