Mean squared displacement
= Mean squared displacement
{title2=$\langle|X(t+\tau)-X(t)|^2\rangle$}
A mean squared displacement is the <expected value> of a squared position change over a specified time lag. For isotropic free <diffusion> in $d$ dimensions, it equals $2dD\tau$. A nonzero mean <drift> contributes its squared displacement as well as the displacement <variance>; specifying the tracked coordinates and whether the mean is subtracted is essential.