Comment on “Finite-size scaling of survival probability in branching processes”

Nanxin Wei and Gunnar Pruessner
Phys. Rev. E 94, 066101 – Published 15 December 2016

Abstract

R. Garcia-Millan et al. [Phys. Rev. E 91, 042122 (2015)] reported a universal finite-size scaling form of the survival probability in discrete time branching processes. In this comment, we generalize the argument to a wide range of continuous time branching processes. Owing to the continuity, the resulting differential (rather than difference) equations can be solved in closed form, rendering some approximations by R. Garcia-Millan et al. superfluous, although we work along similar lines. In the case of binary branching, our results are in fact exact. Demonstrating that discrete time and continuous time models have their leading order asymptotics in common, raises the question to what extent corrections are identical.

  • Received 1 July 2016

DOI:https://doi.org/10.1103/PhysRevE.94.066101

©2016 American Physical Society

Authors & Affiliations

Nanxin Wei* and Gunnar Pruessner

  • Department of Mathematics, Imperial College London, 180 Queen's Gate, London SW7 2AZ, United Kingdom

  • *n.wei14@imperial.ac.uk
  • g.pruessner@imperial.ac.uk

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Original Article

Finite-size scaling of survival probability in branching processes

Rosalba Garcia-Millan, Francesc Font-Clos, and Álvaro Corral
Phys. Rev. E 91, 042122 (2015)

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Issue

Vol. 94, Iss. 6 — December 2016

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