Breakdown of the Finite-Time and-Population Scalings of the Large Deviation Function in the Large-Size Limit of a Contact Process

Abstract:

In a recent study (Nemoto et al 2017 Phys. Rev. E 95 012102; Guevara Hidalgo et al 2017 Phys. Rev. E 95 062134), the finite-time (t) and-population size (N c) scalings in the evaluation of a large deviation function (LDF) estimator were analyzed by means of the cloning algorithm. These scalings provide valuable information about the convergence of the LDF estimator in the infinite-t and infinite-N c limits. For the cases analyzed in that study, the scalings of the systematic errors of the estimator were found to behave as t− 1 and in the large-t and large-N c asymptotics. Moreover, it was shown how this convergence speed can be used in order to extract an asymptotic limit which rendered a better LDF estimation in comparison to the standard estimator. However, the validity of these scaling laws, and thus the convergence of the estimator, was proved only in systems for which the number of sites L (where the dynamics …

Año de publicación:

2018

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Fuente:

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