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

International audienceWe consider the Kob Andersen model, a cooperative lattice gas with kinetic constraints which has been widely analysed in the physics literature in connection with the study of the liquid/glass transition. Cooperative here means that the facilitating sites (the vacancies) must collectively cooperate in order to ensure global motion of the particles. Our main result, which significantly improves upon previous ones, is a pure diffusive scaling of the relaxation time $T_\text{rel}(L)\approx L^2$ in a finite box of side $L$ of $\mathbb{Z}^d$, $d\ge 2,$ with sources at the boundary. The main tools combine a recent set of ideas and techniques developed to establish universality results for kinetically constrained spin models, with methods from oriented percolation and canonical flows for Markov chains