K I Hopcraft et al 2004 J. Phys. A: Math. Gen. 37 L635 doi:10.1088/0305-4470/37/48/L01
K I Hopcraft, E Jakeman and J O Matthews
Show affiliationsConsideration is given to the convergence properties of sums of identical, independently distributed random variables drawn from a class of discrete distributions with power-law tails, which are relevant to scale-free networks. Different limiting distributions, and rates of convergence to these limits, are identified and depend on the index of the tail. For indices ≥2, the topology evolves to a random Poisson network, but the rate of convergence can be extraordinarily slow and unlikely to be yet evident for the current size of the WWW for example. It is shown that treating discrete scale-free behaviour with continuum or mean-field approximations can lead to incorrect results.
89.75.Hc Networks and genealogical trees
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
Issue 48 (3 December 2004)
Received 21 September 2004, in final form 22 October 2004
Published 17 November 2004
K I Hopcraft et al 2004 J. Phys. A: Math. Gen. 37 L635
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