Abstract
© 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 language | English |
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Article number | 042122 |
Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |
Volume | 91 |
Issue number | 4 |
DOIs | |
Publication status | Published - 20 Apr 2015 |