Phase transition, scaling of moments, and order-parameter distributions in Brownian particles and branching processes with finite-size effects.

@article{Corral2018PhaseTS,
  title={Phase transition, scaling of moments, and order-parameter distributions in Brownian particles and branching processes with finite-size effects.},
  author={{\'A}. Corral and Rosalba Garcia-Millan and N. Moloney and Francesc Font-Clos},
  journal={Physical review. E},
  year={2018},
  volume={97 6-1},
  pages={
          062156
        }
}
We revisit the problem of Brownian diffusion with drift in order to study finite-size effects in the geometric Galton-Watson branching process. This is possible because of an exact mapping between one-dimensional random walks and geometric branching processes, known as the Harris walk. In this way, first-passage times of Brownian particles are equivalent to sizes of trees in the branching process (up to a factor of proportionality). Brownian particles that reach a distant reflecting boundary… Expand
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