Convergence in Flat-Histogram Sampling

A density of states (DOS) specified by a polynomial has been used to investigate flat-histogram sampling for continuous values of the energy. The squared deviation of the normalized walker histogram around the ideal value of unity is found to give a good description of the self-consistency of the estimated DOS used for the sampling. For converged values of the estimated DOS, the χ2 difference from the specified DOS decreases as the inverse of the number of samples. The Gamma distribution is found to describe the range of convergence for different specific random walks towards convergence of the DOS.