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 Pro

Presents the zaia usage as premium feature

ZAIA

Presents AI Discovery search usage as a premium feature

AI Discovery

Presents AI Discovery explain and summary usage as a premium feature

Content Analysis

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Presents the pdf analysis as premium feature

PDF Analysis

1500 Top-up

3000 Top-up

Zendy Basic

2500 Top-up

Zendy Unlimited

Presents the access of premium content as premium feature

Premium Content

We consider the Kob-Andersen model, a cooperative lattice gas with kineticconstraints which has been widely analyzed in the physics literature inconnection with the study of the liquid/glass transition. We consider the modelin a finite box of linear size $L$ with sources at the boundary. Our result,which holds in any dimension and significantly improves upon previous ones,establishes for any positive vacancy density $q$ a purely diffusive scaling ofthe relaxation time $T_{\rm rel}$ of the system. Furthermore, as $q\downarrow0$ we prove upper and lower bounds on $L^{-2} T_{\rm rel} (q,L)$ which agreewith the physicists belief that the dominant equilibration mechanism is acooperative motion of rare large droplets of vacancies. The main tools combinea recent set of ideas and techniques developed to establish universalityresults for kinetically constrained spin models, with methods from bootstrappercolation, oriented percolation and canonical flows for Markov chains.

Diffusive scaling of the Kob-Andersen model in $\mathbb{Z}^d$