title: Finite-size scaling of survival probability in branching processes.
abstract: 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)=2ye(y)/(e(y)-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.
authors.affiliation: Departament de Matemàtiques, Facultat de Ciències, Universitat Autònoma de Barcelona, E-08193 Barcelona, Spain.|Departament de Física, Facultat de Ciències, Universitat Autònoma de Barcelona, E-08193 Barcelona, Spain.
authors.forename: Rosalba
authors.initials: R
authors.lastname: Garcia-Millan
authors.affiliation: Departament de Matemàtiques, Facultat de Ciències, Universitat Autònoma de Barcelona, E-08193 Barcelona, Spain.|Centre de Recerca Matemàtica, Edifici C, Campus Bellaterra, E-08193 Barcelona, Spain.
authors.forename: Francesc
authors.initials: F
authors.lastname: Font-Clos
authors.affiliation: Departament de Matemàtiques, Facultat de Ciències, Universitat Autònoma de Barcelona, E-08193 Barcelona, Spain.|Centre de Recerca Matemàtica, Edifici C, Campus Bellaterra, E-08193 Barcelona, Spain.
authors.forename: Álvaro
authors.initials: Á
authors.lastname: Corral
mesh_terms: D003198:Computer Simulation; D008962:Models, Theoretical; D044367:Phase Transition; D011336:Probability