Cluster tails for critical power-law inhomogeneous random graphs

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Recently, the scaling limit of cluster sizes for critical inhomogeneous random graphs of rank-1 type having finite variance but in finite third moment degrees was obtained. It was proved that when the degrees obey a power law with exponent $ \tau \in (3,4) $, the sequence of clusters ordered in decreasing size and multiplied through by $ n^{ -(\tau -2) / (\tau -1) } $ converges as $ n \rightarrow \infty $ to a sequence of decreasing non-degenerate random variables. Here, we study the tails of the limit of the rescaled largest cluster, i.e., the probability that the scaling limit of the largest cluster takes a large value u, as a function of u. This extends a related result of Pittel for the Erdös-Rényi random graph to the setting of rank-1 inhomogeneous random graphs with infinite third moment degrees. We make use of delicate large deviations and weak convergence arguments.
Originele taal-2Engels
Plaats van productieEindhoven
UitgeverijEurandom
Aantal pagina's44
StatusGepubliceerd - 2014

Publicatie series

NaamReport Eurandom
Volume2014007
ISSN van geprinte versie1389-2355

Vingerafdruk

Random Graphs
Tail
Power Law
Scaling Limit
Moment
Finite Type
Weak Convergence
Large Deviations
Random variable
Exponent
Converge

Citeer dit

Hofstad, van der, R. W., Kliem, S. M., & Leeuwaarden, van, J. S. H. (2014). Cluster tails for critical power-law inhomogeneous random graphs. (Report Eurandom; Vol. 2014007). Eindhoven: Eurandom.
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Cluster tails for critical power-law inhomogeneous random graphs. / Hofstad, van der, R.W.; Kliem, S.M.; Leeuwaarden, van, J.S.H.

Eindhoven : Eurandom, 2014. 44 blz. (Report Eurandom; Vol. 2014007).

Onderzoeksoutput: Boek/rapportRapportAcademic

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