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Brownian motion speeds.

  1. May 1, 2005 #1
    Consider the density probability function following the diffusion equation with diffusion parameter D, with the initial condition [tex] f(x,t=0)=\delta(x) [/tex] :

    [tex] f(x,t)=\frac{e^{-\frac{x^2}{4Dt}}}{\sqrt{4\pi Dt}} [/tex]

    From this : if t=0, then the particle is at x=0.

    Consider a very small t>0...then we get [tex] P(A<x<A+dx)>0 \forall A>0, dx>0 [/tex].

    Which means that : the particle has a non-vanishing prob. of having travelled a distance as big as you want in a time as small as you want.

    Does anybody know if relativistic brownian motion was studied ?

    There the function f should be compact...or something like that ?
  2. jcsd
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