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The Wang-Landau algorithm aims at sampling from a probability distribution,while penalizing some regions of the state space and favoring others. It iswidely used, but its convergence properties are still unknown. We show that forsome variations of the algorithm, the Wang-Landau algorithm reaches theso-called flat histogram criterion in finite time, and that this criterion canbe never reached for other variations. The arguments are shown in a simplecontext - compact spaces, density functions bounded from both sides - for thesake of clarity, and could be extended to more general contexts.

The Wang-Landau algorithm reaches the flat histogram criterion in finite time