Tauberian Theory for Multivariate Regularly Varying Distributions with Application to Preferential Attachment Networks

Abel-Tauberian theorems relate power law behavior of distributions and their transforms. We formulate and prove a multivariate version for non-standard regularly varying measures on $\mathbb{R}_+^p$ and then apply it to prove that the joint distribution of in- and out-degree in a directed edge preferential attachement model has jointly regularly varying tails.

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