= Radial Brownian displacement
{title2=$\sqrt{\langle|\Delta\mathbf r|^2\rangle}=\sqrt{6Dt}$}
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.
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