English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

Let $\bb T_L = \bb Z/L \bb Z$ be the one-dimensional torus with $L$ points.For $\alpha >0$, 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 the totally asymmetric zero rangeprocess on $\bb T_L$ in which a particle jumps from a site $x$, occupied by $k$particles, to the site $x+1$ at rate $g(k)$. Let $N$ stand for the total numberof particles. In the stationary state, if $\alpha >1$, as $N\uparrow\infty$,all particles but a finite number accumulate on one single site. We show inthis article that in the time scale $N^{1+\alpha}$ the site which concentratesalmost all particles evolves as a random walk on $\bb T_L$ whose transitionrates are proportional to the capacities of the underlying random walk,extending to the asymmetric case the results obtained in \cite{bl3} forreversible zero-range processes on finite sets.

Metastability for a non-reversible dynamics: the evolution of the condensate in totally asymmetric zero range processes