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Pré-Publication, Document De Travail Année : 2009

Metastability of reversible condensed zero range processes on a finite set

Résumé

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.
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Dates et versions

hal-00425463 , version 1 (21-10-2009)

Identifiants

  • HAL Id : hal-00425463 , version 1

Citer

Johel Beltran, Claudio Landim. Metastability of reversible condensed zero range processes on a finite set. 2009. ⟨hal-00425463⟩
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