Efficiency of the Wang-Landau algorithm: a simple test case (Q2927897)

The Wang-Landau algorithm is an adaptive importance Markov chain Monte Carlo (MCMC) technique based on a single trajectory interacting with its own past. The authors analyze the efficiency of this algorithm in escaping metastable states. Analytic results are presented for a toy model with only three states (two metastable states and one intermediate state which is visited with a low probability). Numerical results are discussed for a 2D-model from computational statistical physics. It is shown that in these examples the exit times from metastable states are much smaller for the Wang-Landau algorithm than for the standard Metropolis-Hastings algorithm.