Radial Brownian displacement ($\sqrt{⟨|\Delta \mathbf{r}{|}^2⟩}=\sqrt{6Dt}$)

For isotropic three-dimensional diffusion with coefficient $D$, the vector mean displacement is zero, the radial RMS is $\sqrt{6Dt}$ and the mean radial magnitude is $4\sqrt{Dt/\pi }$. The radial distribution is the Maxwell speed distribution arising from three independent Gaussian coordinate increments. State the statistic before calling a quantity an average distance; it is not the cumulative path length.