SIAM Journal on Mathematical Analysis
We prove that uniformly random packings of copies of a certain simply connected figure in the plane exhibit global connectedness at all sufficiently high densities, but not at low densities.
Bowen, L.; Lyons, R.; Radin, C.; and Winkler, P., "A Solidification Phenomenon in Random Packings" (2006). Open Dartmouth: Faculty Open Access Articles. 2470.