We present a mathematical analysis of the Wang-Landau algorithm, prove its convergence, identify sources of errors and strategies for optimization. In particular, we found the histogram increases uniformly with small fluctuation after a stage of initial accumulation, and the statistical error is found to scale as $\sqrt{ \ln f}$ with the modification factor $f$. This has implications for strategies for obtaining fast convergence.
Categories: cond-mat.stat-mech