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Phys Rev E. 2017 Jun;95(6-1):062134. doi: 10.1103/PhysRevE.95.062134. Epub 2017 Jun 28.

Finite-time and finite-size scalings in the evaluation of large-deviation functions: Numerical approach in continuous time.

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Institut Jacques Monod, CNRS UMR 7592, Université Paris Diderot, Sorbonne Paris Cité, F-750205, Paris, France.
Laboratoire de Probabilités et Modèles Aléatoires, Sorbonne Paris Cité, UMR 7599 CNRS, Université Paris Diderot, 75013 Paris, France.
Philippe Meyer Institute for Theoretical Physics, Physics Department, École Normale Supérieure and PSL Research University, 24 rue Lhomond, 75231 Paris Cedex 05, France.
LIPhy, Université Grenoble Alpes and CNRS, F-38042 Grenoble, France.


Rare trajectories of stochastic systems are important to understand because of their potential impact. However, their properties are by definition difficult to sample directly. Population dynamics provides a numerical tool allowing their study, by means of simulating a large number of copies of the system, which are subjected to selection rules that favor the rare trajectories of interest. Such algorithms are plagued by finite simulation time and finite population size, effects that can render their use delicate. In this paper, we present a numerical approach which uses the finite-time and finite-size scalings of estimators of the large deviation functions associated to the distribution of rare trajectories. The method we propose allows one to extract the infinite-time and infinite-size limit of these estimators, which-as shown on the contact process-provides a significant improvement of the large deviation function estimators compared to the standard one.


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