Random cages formed by hard spheres encode how local confinement evolves toward jamming. This work develops a minimal infinite-dimensional model and tests its finite-dimensional behavior, clarifying which geometric features survive across dimensions and how they place jamming algorithms in a common universality class.
A minimal model with random planes is used to isolate the geometry of cage formation and to understand how glass-like confinement emerges.
This paper compares jamming algorithms in the random Lorentz gas and shows how their geometric structure affects the resulting jammed states.