Convergence of the Wang-Landau algorithm

TL;DR

This paper proves the convergence and establishes a central limit theorem for the Wang-Landau algorithm, an adaptive sampling method used to improve Markov Chain Monte Carlo sampling in metastable systems.

Contribution

It provides the first rigorous proof of convergence and a central limit theorem for the Wang-Landau algorithm, advancing theoretical understanding.

Findings

Proves convergence of the Wang-Landau algorithm

Establishes a central limit theorem for the algorithm

Enhances theoretical foundation for adaptive importance sampling

Abstract

We analyze the convergence properties of the Wang-Landau algorithm. This sampling method belongs to the general class of adaptive importance sampling strategies which use the free energy along a chosen reaction coordinate as a bias. Such algorithms are very helpful to enhance the sampling properties of Markov Chain Monte Carlo algorithms, when the dynamics is metastable. We prove the convergence of the Wang-Landau algorithm and an associated central limit theorem.