Finite-Time and -Size Scalings in the Evaluation of Large Deviation Functions Part I: 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 observ-ables. 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.
Type de document :
Pré-publication, Document de travail
12 pages, 1 figure. First part of pair of companion papers, Part II being arXiv:1607.08804. 2016
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Contributeur : Vivien Lecomte <>
Soumis le : mardi 2 août 2016 - 10:41:37
Dernière modification le : jeudi 13 octobre 2016 - 15:49:19
Document(s) archivé(s) le : mardi 8 novembre 2016 - 19:40:20

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  • HAL Id : hal-01350893, version 1
  • ARXIV : 1607.04752

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Takahiro Nemoto, Esteban Guevara Hidalgo, Vivien Lecomte. Finite-Time and -Size Scalings in the Evaluation of Large Deviation Functions Part I: Analytical Study using a Birth-Death Process. 12 pages, 1 figure. First part of pair of companion papers, Part II being arXiv:1607.08804. 2016. <hal-01350893>

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