Extremes of Sums and Maxima with Application to Random Networks

The sums and maxima of non-stationary random length sequences of regularly varying random variables may have the same tail and extremal indices, Markovich and Rodionov (2020). The main constraint is that there exists a unique series in a scheme of series with the minimum tail index. The result is now revised allowing a random bounded number of series to have the minimum tail index. This is applied to random networks.