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Mean squared distance traveled by an unbiased random walker in 1-D?

  1. Feb 12, 2014 #1
    Hey!

    I've been doing some research on random walks. From what I have gathered, a random walker in 1-D will have:
    <x> = N l (2 p - 1)

    σ = 2 l sqrt[N p (1 - p) ]

    Here, N is the number of steps, p is the probability to take a step to the right and l is the step size.
    I was wondering what <x^2> would be. From what I found, it seems to be l sqrt(N) but when I try to use <x^2> = σ^2 + <x>^2 , I dont get l sqrt(N) . I would like to know what <x^2> really is for an unbiased random walk.

    Thanks
     
    Last edited: Feb 12, 2014
  2. jcsd
  3. Feb 12, 2014 #2

    mathman

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    In "l sqrt(N)", what is "l"?
     
  4. Feb 13, 2014 #3
    l is the step size here.
     
  5. Feb 13, 2014 #4

    mathman

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    The second moment is proportional to l^2. In general its main use is as an intermediate to get the variance.
     
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