Finite-Time and -Size Scalings in the Evaluation of Large Deviation Functions - Part I: Analytical Study using a Birth-Death Process

Takahiro Nemoto, Esteban Guevara Hidalgo, Vivien Lecomte

Published 2016-07-16Version 1

The Giardin\`a-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 simple two-state model.