2019/05/13 by Caputo, Pietro, Quattropani, Matteo · 1 citation
#05C81 #60J10 #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.1905.04993
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.