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.

13 pages, 6 figures. v2: corrections focusing the paper on large deviations; v3: minor corrections, close to published version

References in corpus (20)

• Theoretical perspective on the glass transition and amorphous materials
• The large deviation approach to statistical mechanics
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Rare events and the convergence of exponentially averaged work values
• Experimental Free Energy Surface Reconstruction From Single-Molecule Force Spectroscopy Using Jarzynski's Equality
• A numerical approach to large deviations in continuous-time
• Probing rare physical trajectories with Lyapunov weighted dynamics
• Asymptotics of superstatistics
• Experimental free energy measurements of kinetic molecular states using fluctuation theorems
• Escorted Free Energy Simulations: Improving Convergence by Reducing Dissipation
• Optimized free energies from bidirectional single-molecule force spectroscopy
• Thermodynamics of currents in nonequilibrium diffusive systems: theory and simulation
• Symmetry properties of the large-deviation function of the velocity of a self-propelled polar particle
• DMRG-study of current and activity fluctuations near non-equilibrium phase transitions
• Current Fluctuations and Statistics During a Large Deviation Event in an Exactly-Solvable Transport Model
• Uncovering latent singularities from multifractal scaling laws in mixed asymptotic regime. Application to turbulence
• Anisotropic Isometric Fluctuation Relations in experiment and theory on a self-propelled rod
• Dispersion in the large-deviation regime. Part I: shear flows and periodic flows
• Methods for calculating nonconcave entropies
• Linearization effect in multifractal analysis: Insights from the Random Energy Model

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