Unfortunately, it turned out that the narrow Gaussian velocity phase distribution achieves the leptocurtic behaviour by an unrealistic mechanism: The momentary velocity (in x- and y-directions) has a strong peak exactly at the center of the simulation time interval:

This leads to a huge step in the displacements:

This in turn leads to some isolated contributions in the far tail of the step width distribution, which causes the positive cutosis.

This is not what we are looking for.
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