title: Finite-time and finite-size scalings in the evaluation of large-deviation functions: Analytical study using a birth-death process.
abstract: The Giardinà-Kurchan-Peliti algorithm is a numerical procedure that uses population dynamics in order to calculate large deviation functions associated to the distribution of time-averaged observables. To study the numerical errors of this algorithm, we explicitly devise a stochastic birth-death process that describes the time evolution of the population probability. From this formulation, we derive that systematic errors of the algorithm decrease proportionally to the inverse of the population size. Based on this observation, we propose a simple interpolation technique for the better estimation of large deviation functions. The approach we present is detailed explicitly in a two-state model.
authors.affiliation: Laboratoire de Probabilités et Modèles Aléatoires, Sorbonne Paris Cité, UMR 7599 CNRS, Université Paris Diderot, 75013 Paris, France.
authors.forename: Takahiro
authors.initials: T
authors.lastname: Nemoto
authors.affiliation: Laboratoire de Probabilités et Modèles Aléatoires, Sorbonne Paris Cité, UMR 7599 CNRS, Université Paris Diderot, 75013 Paris, France.|Institut Jacques Monod, CNRS UMR 7592, Université Paris Diderot, Sorbonne Paris Cité, F-750205, Paris, France.
authors.forename: Esteban
authors.initials: E
authors.lastname: Guevara Hidalgo
authors.affiliation: Laboratoire de Probabilités et Modèles Aléatoires, Sorbonne Paris Cité, UMR 7599 CNRS, Université Paris Diderot, 75013 Paris, France.
authors.forename: Vivien
authors.initials: V
authors.lastname: Lecomte
mesh_terms: D000465:Algorithms; D000818:Animals; D020342:Finite Element Analysis; D008954:Models, Biological; D015233:Models, Statistical; D009026:Mortality; D036801:Parturition; D011157:Population Dynamics; D011336:Probability; D013269:Stochastic Processes