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Branching annihilating random walk on random regular graphs

Szabo1

  • 1Research Institute for Technical Physics and Materials Science, P.O. Box 49, H-1525 Budapest, Hungary.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|December 2, 2000
PubMed
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The branching annihilating random walk on random graphs shows concentration decreasing with branching rate for z>=4 neighbors. For z=3 neighbors, this relationship changes, indicating graph structure impacts particle dynamics.

Area of Science:

  • Statistical Physics
  • Complex Systems
  • Network Science

Background:

  • The branching annihilating random walk (BARW) is a model for systems with particle creation and destruction.
  • Understanding particle dynamics on complex networks like random graphs is crucial for various scientific fields.

Purpose of the Study:

  • To investigate the behavior of BARW on random graphs with a uniform degree (z).
  • To analyze the impact of branching rate and graph connectivity on particle concentration.

Main Methods:

  • Utilized Monte Carlo simulations to model the BARW process.
  • Employed generalized mean-field analysis and a modified mean-field theory.
  • Incorporated the probability of mutual annihilation and single-walker return features.

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Main Results:

  • Observed a linear decrease in particle concentration with the branching rate for random graphs with z>=4 neighbors.
  • Found that the coefficient of the linear term becomes zero for z=3 neighbors.
  • The modified mean-field theory accurately describes these observed properties.

Conclusions:

  • Graph connectivity significantly influences BARW dynamics.
  • The transition at z=3 highlights the importance of local graph structure in annihilation processes.
  • The study provides a refined theoretical framework for BARW on random graphs.