The scale-free conjecture for infinity-PageRank

Let $G$ be a graph with vertex set $V(G)$, and let $d_i$ be the degree of node $i\in V(G)$. Suppose

$$d_i\sim X,$$

where $X$ is a regularly varying random variable. Let $PR_\infty(i)$ denote the infinity-PageRank value of node $i$.

Scale-free infinity-PageRank conjecture. If $d_i\sim X$ where $X$ is a regularly varying random variable, then $PR_\infty(i)$ will also be scale-free.

The conjecture concerns the transfer of heavy-tailed, regularly varying degree behavior to infinity-PageRank values. The source motivates it by similarity with known behavior of standard PageRank, but provides no proof or resolution.