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• W2734448685 abstract "We study the mixing time of random walks on small-world networks modelled as follows: starting with the 2-dimensional periodic grid, each pair of vertices ${u,v}$ with distance $d>1$ is added as a long-range edge with probability proportional to $d^{-r}$, where $rgeq 0$ is a parameter of the model. Kleinberg studied a close variant of this network model and proved that the (decentralised) routing time is $O((log n)^2)$ when $r=2$ and $n^{Omega(1)}$ when $rneq 2$. Here, we prove that the random walk also undergoes a phase transition at $r=2$, but in this case the phase transition is of a different form. We establish that the mixing time is $Theta(log n)$ for $r 2$." @default.
• W2734448685 created "2017-07-21" @default.
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• W2734448685 date "2017-07-08" @default.
• W2734448685 modified "2023-09-27" @default.
• W2734448685 title "Random Walks on Small World Networks" @default.
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