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

Pierre Jacob and Robin Ryder (from Paris-Dauphine, CREST, and Statisfaction) have just arXived (and submitted to the Annals of Applied Probability) a neat result on the Wang-Landau algorithm. (This algorithm, which modifies the target in a sort of reweighted partioned sampling to achieve faster convergence, has always been perplexing to me.)  They show that some variations of the Wang-Landau algorithm meet the flat histogram criterion in finite time, and, just as importantly that other variations do not reach this criterion. The proof uses elegant Markov chain arguments and I hope the paper makes it through, as there are very few theoretical results on this algorithm. (Pierre also wrote recently a paper with Luke Bornn, Arnaud Doucet, and Pierre Del Moral, on An Adaptive Interacting Wang-Landau Algorithm for Automatic Density Exploration last week, with an associated R package. Not yet on CRAN.)