3 problems

Zero self-diffusion conjecture. For hard-core potentials and sufficiently large activities in multi-dimensional grand canonical Gibbs measures, the self-diffusion matrix satisfies

Let $D(q)$ denote the self-diffusion coefficient in the Kob–Andersen model, with constraint parameter and dimension satisfying $k=d=2$, and let $q$ be the vacancy density. Sharp se…

Finite-density transition conjecture. For some KCLG, a diffusive/non-diffusive transition occurs at a finite critical density $\rho_c<1$: the self-diffusion matrix is non-degenerat…