  Recently, Wang and Landau proposed a new random walk algorithm that can be
very efficiently applied to many problems. Subsequently, there has been
numerous studies on the algorithm itself and many proposals for improvements
were put forward. However, fundamental questions such as what determines the
rate of convergence has not been answered. To understand the mechanism behind
the Wang-Landau method, we did an error analysis and found that a steady state
is reached where the fluctuations in the accumulated energy histogram saturate
at values proportional to $[\log(f)]^{-1/2}$. This value is closely related to
the error corrections to the Wang-Landau method. We also study the rate of
convergence using different "tuning" parameters in the algorithm.
