Geometry and dynamics for hierarchical regular networks

@article{Boettcher2008GeometryAD,
  title={Geometry and dynamics for hierarchical regular networks},
  author={S. Boettcher and B. Gonçalves and J. Azaret},
  journal={Journal of Physics A},
  year={2008},
  volume={41},
  pages={335003}
}
  • S. Boettcher, B. Gonçalves, J. Azaret
  • Published 2008
  • Mathematics, Physics
  • Journal of Physics A
  • The recently introduced hierarchical regular networks HN3 and HN4 are analyzed in detail. We use renormalization group arguments to show that HN3, a 3-regular planar graph, has a diameter growing as ! N with the system size, and random walks on HN3 exhibit super-diffusion with an anomalous exponent dw = 2" log2(! ) # 1.306, where ! = ( ! 5+1)/2 = 1.618... is the ‘golden ratio.’ In contrast, HN4, a non-planar 4-regular graph, has a diameter that grows slower than any power of N, yet, faster than… CONTINUE READING
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