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I would assume that after sufficient time steps I get a steady distribution of the position of the walker. This would be equivalent to the probability distribution of finding the walker at some point in the potential.

However, I have yet no idea how to calculate this distribution from some given p(x). I tried to set up a differential equation using the fact that in the steady case the flow from point x to x + dx and back must be zero. However, I would get a pole at x = 0.5 which is pretty useless. I can post the calculation if someone is interested.

I would be glad for every hint how one could solve this problem. Thanks in advance!

Blue2script