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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.
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https://hal.archives-ouvertes.fr/hal-01350893
Contributor : Vivien Lecomte <>
Submitted on : Tuesday, August 2, 2016 - 10:41:37 AM
Last modification on : Friday, April 10, 2020 - 5:31:09 PM
Document(s) archivé(s) le : Tuesday, November 8, 2016 - 7:40:20 PM

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

Citation

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. 2016. ⟨hal-01350893⟩

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