  Let $r: S\times S\to \bb R_+$ be the jump rates of an irreducible random walk
on a finite set $S$, reversible with respect to some probability measure $m$.
For $\alpha >1$, let $g: \bb N\to \bb R_+$ be given by $g(0)=0$, $g(1)=1$,
$g(k) = (k/k-1)^\alpha$, $k\ge 2$. Consider a zero range process on $S$ in
which a particle jumps from a site $x$, occupied by $k$ particles, to a site
$y$ at rate $g(k) r(x,y)$. Let $N$ stand for the total number of particles. In
the stationary state, as $N\uparrow\infty$, all particles but a finite number
accumulate on one single site. We show in this article that in the time scale
$N^{1+\alpha}$ the site which concentrates almost all particles evolves as a
random walk on $S$ whose transition rates are proportional to the capacities of
the underlying random walk.
