  A classical diffusion model of Ehrenfest which consists of $2$-urns and
$n$-balls is realized by a finite Gelfand pair $(H_{n},S_{n})$, where $H_{n}$
is the hyperoctahedral group and $S_{n}$ is the symmetric group. This fact can
be generalized to multi-urn version by using Gelfand pairs of complex
reflection groups.
