Abstract
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 attachment model has jointly regularly varying tails.
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Resnick, S., Samorodnitsky, G. Tauberian theory for multivariate regularly varying distributions with application to preferential attachment networks. Extremes 18, 349–367 (2015). https://doi.org/10.1007/s10687-015-0216-2
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DOI: https://doi.org/10.1007/s10687-015-0216-2