Diameter of the Stochastic Mean-Field Model of Distance
2017 ◽
Vol 26
(6)
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pp. 797-825
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We consider the complete graph 𝜅n on n vertices with exponential mean n edge lengths. Writing Cij for the weight of the smallest-weight path between vertices i, j ∈ [n], Janson [18] showed that maxi,j∈[n]Cij/logn converges in probability to 3. We extend these results by showing that maxi,j∈[n]Cij − 3 logn converges in distribution to some limiting random variable that can be identified via a maximization procedure on a limiting infinite random structure. Interestingly, this limiting random variable has also appeared as the weak limit of the re-centred graph diameter of the barely supercritical Erdős–Rényi random graph in [22].
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2014 ◽
Vol 2014
(1)
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pp. 13D02-0
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2011 ◽
Vol 20
(08)
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pp. 1663-1675
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Keyword(s):
2010 ◽
Vol 74
(6)
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pp. 850-853
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Keyword(s):
Keyword(s):
2010 ◽
Vol 525
(1)
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pp. 29-40
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Keyword(s):
2014 ◽
pp. 297-314
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