Papers › Mixing time of PageRank surfers on sparse random digraphs
Mixing time of PageRank surfers on sparse random digraphs
Pietro Caputo, Matteo Quattropani
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We consider the generalised PageRank walk on a digraph G, with refresh probability α and resampling distribution λ. We analyse convergence to stationarity when G is a large sparse random digraph with given degree sequences, in the limit of vanishing α. We identify three scenarios: when α is much smaller than the inverse of the mixing time of G the relaxation to equilibrium is dominated by the simple random walk and displays a cutoff behaviour; when α is much larger than the inverse of the mixing time of G on the contrary one has pure exponential decay with rate α; when α 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 uniformly in the resampling distribution λ.
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