Mixing time of PageRank surfers on sparse random digraphs. Issue 3 (12th April 2021) - Caputo, Pietro; Quattropani, Matteo
Abstract: We consider the generalized PageRank walk on a digraph G, with refresh probability α and resampling distribution λ . We analyze 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 behavior; 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 behavior interpolating between cutoff and exponential decay. This trichotomy is shown to hold uniformly in the starting point and uniformly in the resampling distribution λ .