Random Walks on Small World Networks

@article{Dyer2017RandomWO,
  title={Random Walks on Small World Networks},
  author={Martin E. Dyer and Andreas Galanis and Leslie Ann Goldberg and Mark Jerrum and Eric Vigoda},
  journal={ACM Transactions on Algorithms (TALG)},
  year={2017},
  volume={16},
  pages={1 - 33}
}
  • Martin E. Dyer, Andreas Galanis, +2 authors Eric Vigoda
  • Published 2017
  • Computer Science
  • ACM Transactions on Algorithms (TALG)
  • 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 r≥ 0 is a parameter of the model. Kleinberg [33{ studied a close variant of this network model and proved that the (decentralised) routing time is O((log n)2) when r=2 and nΩ (1) when r≠ 2. Here, we prove that the random walk also undergoes a… CONTINUE READING
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