The mean square displacement (MSD) of a set of 
displacements 
is given by
 |
It arises particularly in Brownian motion and random walk problems. For two-dimensional random walks with unit steps taken in random directions, the MSD is given by
 |
Mean Square Displacement
See also
Random Walk--2-DimensionalExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Mean Square Displacement." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MeanSquareDisplacement.html