A Simple Branching Process Approach to the Phase Transition in $G_{n,p}$
Keyword(s):
It is well known that the branching process approach to the study of the random graph $G_{n,p}$ gives a very simple way of understanding the size of the giant component when it is fairly large (of order $\Theta(n)$). Here we show that a variant of this approach works all the way down to the phase transition: we use branching process arguments to give a simple new derivation of the asymptotic size of the largest component whenever $(np-1)^3n\to\infty$.
2015 ◽
Vol 47
(4)
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pp. 973-988
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Keyword(s):
2012 ◽
Vol 49
(3)
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pp. 601-611
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Keyword(s):
2015 ◽
Vol 47
(04)
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pp. 973-988
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2010 ◽
Vol 19
(5-6)
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pp. 835-926
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2008 ◽
Vol 17
(1)
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pp. 67-86
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2012 ◽
Vol 21
(1-2)
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pp. 265-299
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Keyword(s):
2012 ◽
Vol 49
(03)
◽
pp. 601-611
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Keyword(s):
2015 ◽
Vol 51
(2)
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pp. 756-780
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2018 ◽
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