Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Mean squared distance for (persistent) random walks

  1. Mar 1, 2012 #1
    Hi, I'm looking at how to derive the mean-squared-distance from the velocity autocorrelation for a random walk. It is given on this page: http://www.compsoc.man.ac.uk/~lucky/Democritus/Theory/msd2.html

    Near the middle of that page the author says 'defining u'=u+s and integrating over u, results in the following form where the ensemble average has also been taken: ', but I can't seem to figure out how that integral following that statement was derived. I know what the velocity autocorrelation is, but when I set u'=u+s and integrate, it doesn't seem to pop up. Any help would be greatly appreciated.
  2. jcsd
  3. Mar 1, 2012 #2
    Never mind, I figured it out. For the curious, I wrote this mathbin:

    http://mathbin.net/89902 [Broken]
    Last edited by a moderator: May 5, 2017
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook