Biroli, GiulioCharbonneau, PatrickHu, YiIkeda, HarukuniSzamel, GrzegorzZamponi, Francesco2022-05-022022-05-022021-06-071520-61061520-5207https://hdl.handle.net/10161/24975The random Lorentz gas (RLG) is a minimal model of both percolation and glassiness, which leads to a paradox in the infinite-dimensional, <i>d</i> → ∞ limit: the localization transition is then expected to be <i>continuous</i> for the former and <i>discontinuous</i> for the latter. As a putative resolution, we have recently suggested that, as <i>d</i> increases, the behavior of the RLG converges to the glassy description and that percolation physics is recovered thanks to finite-<i>d</i> perturbative and nonperturbative (instantonic) corrections [Biroli et al. <i>Phys. Rev. E</i> 2021, 103, L030104]. Here, we expand on the <i>d</i> → ∞ physics by considering a simpler static solution as well as the dynamical solution of the RLG. Comparing the 1/<i>d</i> 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 <i>d</i> → ∞ RLG. These insights help chart a path toward a complete description of finite-dimensional glasses.cond-mat.dis-nncond-mat.dis-nncond-mat.softcond-mat.stat-mechJournal article2022-05-02