## Monday, April 7, 2008

### [AD 6] Gaussian Velocity Phase Distributions

The result [AD 4] does not mean that PL-VAC cannot produce positive kurtosis. To check that, noise is completely turned off for the time being.

Starting from a particular trajectory with pure PL-VAC that showed a slightly positive kurtosis, the phases have been optimized in an evolutionary procedure (mutation + selection). By inspecting the increasingly leptocurtic trajectories, it turned out that their phase distribution evolved from the initial box [-pi,+pi] to something narrower and Gaussian-like.

The following graph shows kurtosis vs lag-time for Gaussian phase distributions, centered around zero and with varying FWHM:

That means that leptocurtic behaviour can be adjusted simply by the FWHM parameter. So our stochastic process is characterized by 4 parameters totally.