  Consider $a$ particles performing simple, symmetric, non-intersecting random
walks, starting at points $2(j-1)$, $1\le j\le a$ at time 0 and ending at
$2(j-1)+c-b$ at time $b+c$. This can also be interpreted as a random rhombus
tiling of an $abc$-hexagon, or as a random boxed planar partition confined to a
rectangular box with side lengths $a$, $b$ and $c$. The positions of the
particles at all times gives a determinantal point process with a correlation
kernel given in terms of the associated Hahn polynomials. In a suitable scaling
limit we obtain non-intersecting Brownian motions which can be related to
Dysons's Hermitian Brownian motion via a suitable transformation.
