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] :(adsbygoogle = window.adsbygoogle || []).push({});

[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 ?

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# Brownian motion speeds.

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