Talk:Random walk
From Academic Kids
Actually, the average distance after n steps is of the order of <math>\sqrt{n}<math> for practically any definition of average. So the original formulation was quite correct. I made some "compromise" with Miguel, but thinking about it, maybe this sentence can be just removed? What do you say?
- You're probably right, except that the root-mean-square is *exactly* sqrt n. I wouldn't remove it, it is one of those intuitive statements that are useful to know. Note that I did not replace "average" by "root-mean-square", but rather supplemented the nontechnical statement with a technical one. — Miguel 18:17, 16 Jul 2004 (UTC)
- Can someone show a proof that the rms is exactly sqrt n? This is not a Poisson distribution, it's a random walk - see e.g. http://mathworld.wolfram.com/RandomWalk1-Dimensional.html and i seem to have a simple proof that it's wrong:
- The (absolute) distance x after n steps can be anywhere in the range from 0 to n inclusive. Taking the definition from root-mean-square, the only way that xrms can equal sqrt n is if xi = n for every i. This is clearly wrong, since xi should range from 0 to n (with probabilities related to the binomial distribution). Therefore xrms must be strictly less than sqrt n. QED.
- So i've modified the rms statement. Please show that my proof is wrong and the sqrt n is right if you wish to reinstate the exactly claim. Boud 13:38, 29 Apr 2005 (UTC)
Stricto Sensu
Well, I didn't really see the point here. A graph is a graphic representation of something and there is no "strict sense" in which it has to be one way or the other. The time axis is just as important as the space axis. Could you please clarify? Gadykozma 05:17, 24 Jul 2004 (UTC)
Well, the walk takes place in space, so it is only "upwards" or "downwards". It gets difficult for beginners to grasp this if they only see the planar representation. But I may be overly cautios and punctillious. Pfortuny 10:14, 24 Jul 2004 (UTC)
