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      Superdiffusion in a class of networks with marginal long-range connections

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          Abstract

          A class of cubic networks composed of a regular one-dimensional lattice and a set of long-range links is introduced. Networks parametrized by a positive integer k are constructed by starting from a one-dimensional lattice and iteratively connecting each site of degree 2 with a \(k\)th neighboring site of degree 2. Specifying the way pairs of sites to be connected are selected, various random and regular networks are defined, all of which have a power-law edge-length distribution of the form \(P_>(l)\sim l^{-s}\) with the marginal exponent s=1. In all these networks, lengths of shortest paths grow as a power of the distance and random walk is super-diffusive. Applying a renormalization group method, the corresponding shortest-path dimensions and random-walk dimensions are calculated exactly for k=1 networks and for k=2 regular networks; in other cases, they are estimated by numerical methods. Although, s=1 holds for all representatives of this class, the above quantities are found to depend on the details of the structure of networks controlled by k and other parameters.

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          Author and article information

          Journal
          24 May 2008
          2009-01-09
          Article
          10.1103/PhysRevE.78.066106
          0805.3769

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

          Custom metadata
          Phys. Rev. E 78, 066106 (2008)
          10 pages, 9 figures
          cond-mat.dis-nn cond-mat.stat-mech

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