Random Walk, Normal Distribution, Rayleigh, Maxwell Boltzmann, Diffusion Equation.
density function of a Rayleigh distribution can be expressed as where σ is the scale parameter of the distribution. The code below shows that the distance samples of 1000 particles after 1 million steps follow a Rayleigh and a Chi distribution. Note that the ‘fit’ gives almost 2 DoF (= 1.87) for