Finite-Time and -Size Scalings in the Evaluation of Large Deviation Functions Part II: Numerical Approach in Continuous Time

Esteban Guevara Hidalgo (1, 2) , Takahiro Nemoto (2) , Vivien Lecomte (2)

1 IJM (UMR_7592) - Institut Jacques Monod
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

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 provide a numerical tool allowing their study, by means of simulating a large number of copies of the system, which are subjected to a selection rule that favors 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 second part of our study (which follows a companion paper [ arXiv:1607.04752 ] dedicated to an analytical study), we present a numerical approach which verifies and uses the finite-time and finite-size scalings of estimators of the large deviation functions associated to the distribution of the rare trajectories. Using the continuous-time cloning algorithm, we propose a method aimed at extracting the infinite-time and infinite-size limits of the estimator of such large deviation functions in a simple system, where, by comparing the numerical results to exact analytical ones, we demonstrate the practical efficiency of our proposed approach.

Domaines: Mécanique statistique [cond-mat.stat-mech]; Physique mathématique [math-ph]

Esteban Guevara Hidalgo, Takahiro Nemoto, Vivien Lecomte. Finite-Time and -Size Scalings in the Evaluation of Large Deviation Functions Part II: Numerical Approach in Continuous Time. Physical Review E , 2017, 95, pp.012102. ⟨10.1103/PhysRevE.95.012102⟩. ⟨hal-01350894⟩