Efficiency of the Wang–Landau algorithm: A simple test case

We analyze the efficiency of the Wang–Landau algorithm to sample a multimodal distribution on a prototypical simple test case. We show that the exit time from a metastable state is much smaller for the Wang–Landau dynamics than for the original standard Metropolis–Hastings algorithm, in some asymptotic regime. Our results are confirmed by numerical experiments on a more realistic test case.