Tauberian Theory for Multivariate Regularly Varying Distributions with Application to Preferential Attachment Networks
Resnick, Sidney; Samorodnitsky, Gennady
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 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.
multivariate heavy tails; preferential attachment model; scale free networks; Tauberian theory