* Claudio Landim (LMRS, Rouen, et IMPA, Rio de Janeiro) - MAP5-UMR 8145

Claudio Landim (LMRS, Rouen, et IMPA, Rio de Janeiro)

Métastabilité du processus de zero range

vendredi 25 janvier 2013, 13h30 - 15h00

Salle de réunion, espace Turing


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.