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 α>1, let g: \bb N\to \bb R_+ be given by g(0)=0, g(1)=1,
g(k)=(k/k−1)α, k≥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↑∞, all particles but a finite number
accumulate on one single site. We show in this article that in the time scale
N1+α 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