Convergence of large deviation estimators

TL;DR

This paper analyzes the convergence properties of large deviation estimators across various stochastic systems, providing conditions for reliable estimation and clarifying previous reports of phase transitions in free energy statistics.

Contribution

It establishes a general framework for the convergence of large deviation estimators, considering boundedness conditions and error definitions, enhancing the reliability of simulation and experimental data analysis.

Findings

Conditions for estimator convergence based on boundedness

Clarification of phase transition reports in free energy estimators

Framework for identifying convergence regions in parameter space

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.