Finite-time and finite-size scalings in the evaluation of large-deviation functions: Analytical study using a birth-death process
Abstract
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 two-state model.
Keywords
Cite
@article{arxiv.1607.04752,
title = {Finite-time and finite-size scalings in the evaluation of large-deviation functions: Analytical study using a birth-death process},
author = {Takahiro Nemoto and Esteban Guevara Hidalgo and Vivien Lecomte},
journal= {arXiv preprint arXiv:1607.04752},
year = {2017}
}
Comments
13 pages, 1 figure. First part of pair of companion papers, Part II being arXiv:1607.08804