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Suppose we have a gas with collisions. The mean free path, $l$, is the average distance a particle travels before colliding with another particle. This is the average, but what is the probability distribution of collisions? It cannot be a Gaussian, because there can be no collisions with $x<0.$ It also cannot be a Poisson distribution, because the distance traveled, $x$, is a real number.

The answer to this question will clearly depend on the nature of interactions between the particles, the (effective) radius of the particles, etc. But I have not found any resource which answers this question from a simple starting point.

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    $\begingroup$ wiki? en.wikipedia.org/wiki/Mean_free_path $d\mathcal{P}(x) = \frac{1}{\ell} e^{-x/\ell} dx$ $\endgroup$
    – warlock
    Commented Oct 12, 2022 at 22:13
  • $\begingroup$ @warlock I do not see a probability distribution on the wiki for the cases I am interested in $\endgroup$
    – Jbag1212
    Commented Oct 13, 2022 at 3:39
  • $\begingroup$ so what is wrong with the distribution I quoted? $\endgroup$
    – warlock
    Commented Oct 13, 2022 at 13:53

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