Finite-size scaling of survival probability in branching processes

Rosalba Garcia-Millan, Francesc Font-Clos, Álvaro Corral

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    8 Citations (Scopus)


    © 2015 American Physical Society. Branching processes pervade many models in statistical physics. We investigate the survival probability of a Galton-Watson branching process after a finite number of generations. We derive analytically the existence of finite-size scaling for the survival probability as a function of the control parameter and the maximum number of generations, obtaining the critical exponents as well as the exact scaling function, which is G(y)=2yey/(ey-1), with y the rescaled distance to the critical point. Our findings are valid for any branching process of the Galton-Watson type, independently of the distribution of the number of offspring, provided its variance is finite. This proves the universal behavior of the finite-size effects in branching processes, including the universality of the metric factors. The direct relation to mean-field percolation is also discussed.
    Original languageEnglish
    Article number042122
    JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
    Issue number4
    Publication statusPublished - 20 Apr 2015


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