Why does Wang-Landau algotirhm work?

[tomkeus]

I sifted through significant pile of papers related to the Wang-Landau algorithm and I still don't get why does it give correct result for the density of states.

I mean, the way it is presented in the papers, it looks quite arbitrary. On the start I have the partition function [tex]Z(\beta)=\sum_E \rho(E)e^{-\beta E}[/tex] and few paragraphs later I have the histogram [tex]h(E)[/tex] and the multipliers [tex]f[/tex].

I don't understand why when the histogram is going flat, the probability density goes to the equilibrium value and why is update of the density of states performed by multiplication with [tex]f[/tex].

 

[Evalesco]

It sounds like you have done a lot of work in trying to understand the Wang-Landau algorithm. I had a similar experience when I tried to wrap my head around it. It can be difficult to understand, especially because it is not your typical algorithm.

At a basic level, the idea behind the Wang-Landau algorithm is that it uses a "flat histogram" technique, which means it keeps a histogram of the energies of each state that is explored and uses this information to update the density of states. By making sure the histogram is flat, the algorithm can ensure that it is sampling the entire energy space with equal probability, thus getting an accurate estimate of the density of states.

The key point to remember here is that the multiplication with f is what helps to keep the histogram flat and keep the distribution of energies equal. In the end, when the histogram is flat, the probability density should go to the equilibrium value, which is the exact density of states for the system.

I hope this helps to clear up some of the confusion. If you need any more help understanding the Wang-Landau algorithm, feel free to ask.