title: Convergence of large-deviation estimators.
abstract: We study the convergence of statistical estimators used in the estimation of large-deviation functions describing the fluctuations of equilibrium, nonequilibrium, and manmade stochastic systems. We give conditions for the convergence of these estimators with sample size, based on the boundedness or unboundedness of the quantity sampled, and discuss how statistical errors should be defined in different parts of the convergence region. Our results shed light on previous reports of "phase transitions" in the statistics of free energy estimators and establish a general framework for reliably estimating large-deviation functions from simulation and experimental data and identifying parameter regions where this estimation converges.
authors.affiliation: Max-Planck-Institut für Intelligente Systeme, Heisenbergstraße 3, D-70569 Stuttgart, Germany.|Institut für Theoretische Physik IV, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany.|Department of Physics and Institute of Theoretical Physics, Stellenbosch University, Stellenbosch 7600, South Africa.
authors.forename: Christian M
authors.initials: CM
authors.lastname: Rohwer
authors.affiliation: National Institute for Theoretical Physics (NITheP), Stellenbosch 7600, South Africa.
authors.forename: Florian
authors.initials: F
authors.lastname: Angeletti
authors.affiliation: Department of Physics and Institute of Theoretical Physics, Stellenbosch University, Stellenbosch 7600, South Africa.|National Institute for Theoretical Physics (NITheP), Stellenbosch 7600, South Africa.
authors.forename: Hugo
authors.initials: H
authors.lastname: Touchette