Infinite-mean initial-degree conjecture for the PARID model

Let r_k_{k\geq 1} be the distribution of the initial degrees in the PARID model, and suppose that it is a power-law distribution with exponent $\tau_{\scriptscriptstyle {\rm W}}\in(1,2)$. PARID infinite-mean conjecture. The degree sequence in the PARID model obeys a power law with the same exponent $\tau_{\scriptscriptstyle {\rm W}}$. Since $\tau_{\scriptscriptstyle {\rm W}}\in(1,2)$, the initial-degree distribution has infinite mean; the paper conjectures that its exponent determines the resulting degree sequence in this regime.