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. 
Sidney Resnick and Gennady Samorodnitsky
math.PR