TOPICS
Search

Mean Square Displacement


The mean square displacement (MSD) of a set of N displacements x_n is given by

 <|x|^2>=sum_(k=1)^N|x_k|^2.

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

 <|x|^2>=N.

See also

Random Walk--2-Dimensional

Explore with Wolfram|Alpha

Cite this as:

Weisstein, Eric W. "Mean Square Displacement." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MeanSquareDisplacement.html

Subject classifications