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

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 attachement model has jointly regularly varying tails.

16 pages

References in corpus (1)

• Nonstandard regular variation of in-degree and out-degree in the preferential attachment model

Cited by in corpus (1)

• Invariance principles for operator-scaling Gaussian random fields