Escape of mass in zero-range processes with random rates
| dc.creator | Ferrari, Pablo A. | |
| dc.creator | Sisko, Valentin V. | |
| dc.date | 2006-09-16 | |
| dc.date | 2007-09-06 | |
| dc.date.accessioned | 2026-07-07T08:28:52Z | |
| dc.date.available | 2026-07-07T08:28:52Z | |
| dc.description | We consider zero-range processes in ${\mathbb{Z}}^d$ with site dependent jump rates. The rate for a particle jump from site $x$ to $y$ in ${\mathbb{Z}}^d$ is given by $λ_xg(k)p(y-x)$, where $p(\cdot)$ is a probability in ${\mathbb{Z}}^d$, $g(k)$ is a bounded nondecreasing function of the number $k$ of particles in $x$ and $λ=\{λ_x\}$ is a collection of i.i.d. random variables with values in $(c,1]$, for some $c>0$. For almost every realization of the environment $λ$ the zero-range process has product invariant measures $\{ν_{λ, v}:0\le v\le c\}$ parametrized by $v$, the average total jump rate from any given site. The density of a measure, defined by the asymptotic average number of particles per site, is an increasing function of $v$. There exists a product invariant measure ${ν_{λ, c}}$, with maximal density. Let $μ$ be a probability measure concentrating mass on configurations whose number of particles at site $x$ grows less than exponentially with $\|x\|$. Denoting by $S_λ(t)$ the semigroup of the process, we prove that all weak limits of $\{μS_λ(t),t\ge 0\}$ as $t\to \infty$ are dominated, in the natural partial order, by ${ν_{λ, c}}$. In particular, if $μ$ dominates ${ν_{λ, c}}$, then $μS_λ(t)$ converges to ${ν_{λ, c}}$. The result is particularly striking when the maximal density is finite and the initial measure has a density above the maximal. | |
| dc.description | Published at http://dx.doi.org/10.1214/074921707000000300 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/math/0609469 | |
| dc.identifier | http://arxiv.org/abs/math/0609469 | |
| dc.identifier | IMS Lecture Notes Monograph Series 2007, Vol. 55, 108-120 | |
| dc.identifier | doi:10.1214/074921707000000300 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/137772 | |
| dc.subject | Probability | |
| dc.subject | Mathematical Physics | |
| dc.subject | 60K35, 82C22 (Primary) | |
| dc.title | Escape of mass in zero-range processes with random rates | |
| dc.type | text |