Date:         Thu, 18 Sep 1997 08:17:13 -0400
Reply-To:     Mark Lindeman <mtl4@COLUMBIA.EDU>
Sender:       "SAS(r) Discussion" <SAS-L@UGA.CC.UGA.EDU>
From:         Mark Lindeman <mtl4@COLUMBIA.EDU>
Subject:      Re: random walk redux...
Comments: To: Evan Cooch <cooch@FRASER.SFU.CA>
In-Reply-To:  <341ff561.46256065@newsserver.sfu.ca>
Content-Type: text/plain; charset="us-ascii"

Evan,
 
I am frustrated.  What is your question?
 
>To briefly reiterate, I was working under the assumption that the
>expectation of the mean-square-displacement for a 1-D random walk was
>sqrt(N), where N is the number of steps taken.
 
Actually, as the last page of your notes reiterates, you argue that the
_root_ mean square is sqrt(N), and you are right, and running the
simulation and looking at the std. dev. of "position" will confirm it.
Would it help if I sent you the code to make sure that we're on roughly the
"same page"?
 
However, the last page of your notes is wrong in calling the root mean
square displacement the "average absolute displacement."  These are two
separate concepts (at least if "average" is interpreted as "[arithmetic]
mean").  The average absolute displacement corresponds to the mean of
abs(position), which you correctly derived in SAS as approximately 0.8 of
the root mean square displacement.  As I noted in private mail, this is a
standard feature of normal (or even approximately normal) distributions.
 
If you remain confused, perhaps it is because you're not clear on the
distinction between average absolute displacement and root mean square?
 
Mark Lindeman
MTL4@columbia.edu