  We analyse a mean-field model of Personalized PageRank on the Erdos-Renyi
random graph containing a denser planted Erdos-Renyi subgraph. We investigate
the regimes where the values of Personalized PageRank concentrate around the
mean-field value. We also study the optimization of the damping factor, the
only parameter in Personalized PageRank. Our theoretical results help to
understand the applicability of Personalized PageRank and its limitations for
local graph clustering.
