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

Mixing time of PageRank surfers on sparse random digraphs