Mixing time of PageRank surfers on sparse random digraphs

We consider the generalised PageRank walk on a digraph $G$, with refresh probability $\alpha$ and resampling distribution $\lambda$. analyse convergence to stationarity when $G$ is large sparse random given degree sequences, in limit of vanishing $\alpha$. identify three scenarios: much smaller than inverse mixing time relaxation equilibrium dominated by simple displays cutoff behaviour; larger contrary one has pure exponential decay rate $\alpha$; comparable there mixed behaviour interpolating between decay. This trichotomy shown hold uniformly starting point