Métastabilité du processus de zero range

vendredi 25 janvier 2013, 13h30 - 15h00

$Let r: S\times S\to \bb R_+ be the jump rates of an irreducible$
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
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.