Mixing time of PageRank surfers on sparse random digraphs. Issue 3 (12th April 2021)

• Record Type: Journal Article
• Authors: Caputo, Pietro; Quattropani, Matteo
• Is Part Of: Random structures & algorithms. Volume 59:Issue 3(2021)
• Page Start: 376
• Page End: 406
• Publication Date: 2021-04-12
• Subjects: mixing time -- nonreversible Markov chain -- PageRank -- random digraphs -- random walks on networks; Random graphs -- Periodicals; Mathematical analysis -- Periodicals; 519
• DOI: 10.1002/rsa.21009
• Languages: English
• ISSNs: 1042-9832

Abstract

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 .