Interplay between percolation and glassiness in the random Lorentz gas

The random Lorentz gas (RLG) is a minimal model of transport in heterogeneous media that exhibits continuous localization transition controlled by void space percolation. RLG also provides toy particle caging, which known to be relevant for describing the discontinuous dynamical glasses. In order clarify interplay between seemingly incompatible percolation and caging descriptions RLG, we consider its exact mean-field solution infinite-dimensional $d\ensuremath{\rightarrow}\ensuremath{\infty}$ limit perform numerics $d=2...20$. We find sufficiently high $d$ precedes prevents transition, only happens on timescales diverging with $d$. further show activated processes related rare cage escapes destroy glass finite dimensions, leading rich glassiness physics. This advance suggests can used as develop first-principle description hopping structural