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Deterministic and random partially self-avoiding walks in random media

Author

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  • Terçariol, César Augusto Sangaletti
  • González, Rodrigo Silva
  • Oliveira, Wilnice Tavares Reis
  • Martinez, Alexandre Souto

Abstract

Consider a set of N cities randomly distributed in the bulk of a hypercube with d dimensions. A walker, with memory μ, begins his route from a given city of this map and moves, at each discrete time step, to the nearest point, which has not been visited in the preceding μ steps. After reviewing the more interesting general results, we consider one-dimensional disordered media and show that the walker needs not to have full memory of its trajectory to explore the whole system, it suffices to have memory of order lnN/ln2.

Suggested Citation

  • Terçariol, César Augusto Sangaletti & González, Rodrigo Silva & Oliveira, Wilnice Tavares Reis & Martinez, Alexandre Souto, 2007. "Deterministic and random partially self-avoiding walks in random media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 386(2), pages 678-680.
    • Handle: RePEc:eee:phsmap:v:386:y:2007:i:2:p:678-680
    DOI: 10.1016/j.physa.2007.07.019
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    Cited by:

    1. Merenda, João V.B.S. & Bruno, Odemir M., 2023. "Using deterministic self-avoiding walks as a small-world metric on Watts–Strogatz networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 621(C).

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