Mean-Field Caging in a Random Lorentz Gas.

The random Lorentz gas (RLG) is a minimal model of both percolation and glassiness, which leads to a paradox in the infinite-dimensional, → ∞ limit: the localization transition is then expected to be for the former and for the latter. As a putative resolution, we have recently suggested that, as increases, the behavior of the RLG converges to the glassy description and that percolation physics is recovered thanks to finite- perturbative and nonperturbative (instantonic) corrections [Biroli et al. 2021, 103, L030104]. Here, we expand on the → ∞ physics by considering a simpler static solution as well as the dynamical solution of the RLG. Comparing the 1/ correction of this solution with numerical results reveals that even perturbative corrections fall out of reach of existing theoretical descriptions. Comparing the dynamical solution with the mode-coupling theory (MCT) results further reveals that, although key quantitative features of MCT are far off the mark, it does properly capture the discontinuous nature of the → ∞ RLG. These insights help chart a path toward a complete description of finite-dimensional glasses.