Limit laws for symmetric \(k\)-tensors of regularly varying measures (Q1578060)

Assume that \(X_{1},X_{2},\ldots\) are i.i.d.\ random vectors whose common distribution \(\mu\) is regularly varying. The authors prove that symmetric \(k\)-tensors of the form \(M_{n}=\sum_{i=1}^{n}\otimes^{k}X_{i}\) are asymptotically operator stable, for all \(k\) sufficiently large. Their main technical tools are regular variation and the standard convergence criteria for triangular arrays. They also investigate the structure of the limit distributions and give two applications.