We consider the generalized PageRank walk on a digraph G, with refresh probability and resampling distribution . We analyze convergence to stationarity when G is a large sparse random digraph with given degree sequences, in the limit of vanishing . We identify three scenarios: when 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 is much larger than the inverse of the mixing time of G on the contrary one has pure exponential decay with rate ; when 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 .

中文翻译：

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PageRank 冲浪者在稀疏随机有向图中的混合时间

我们考虑在有向图G上的广义 PageRank 游走，具有刷新概率和重采样分布。当G是具有给定度数序列的大型稀疏随机有向图时，我们分析收敛到平稳性，在消失的极限内。我们确定了三种情况：当G的混合时间的倒数远小于G 时，平衡弛豫由简单随机游走主导并显示截止行为；当远大于G的混合时间的倒数时，相反，它随速率呈指数衰减；when与G的混合时间的倒数相当在截止和指数衰减之间存在混合行为。这种三分法被证明在起点和重采样分布中是一致的 。