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On the growth of a superlinear preferential attachment scheme | | Sunder Sethuraman
; Shankar C. Venkataramani
; | | Date: |
19 Apr 2017 | | Abstract: | We consider an evolving preferential attachment random graph model where at
discrete times a new node is attached to an old node, selected with probability
proportional to a superlinear function of its degree. For such schemes, it is
known that the graph evolution condenses, that is a.s. in the limit graph there
will be a single random node with infinite degree, while all others have finite
degree.
In this note, we establish a.s. law of large numbers type limits and
fluctuation results, as $nuparrowinfty$, for the counts of the number of
nodes with degree $kgeq 1$ at time $ngeq 1$. These limits rigorously verify
and extend a physical picture of Krapivisky, Redner and Leyvraz (2000) on how
the condensation arises with respect to the degree distribution. | | Source: | arXiv, 1704.5568 | | Services: | Forum | Review | PDF | Favorites | |
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