A Solidification Phenomenon in Random Packings

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

A Solidification Phenomenon in Random Packings

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

Percolation of hard disks

Random arrangements of points in the plane, interacting only through a simple hard core exclusion, are considered. An intensity parameter controls the average density of arrangements, in analogy with the Poisson point process. It is proved that at high intensity, an infinite connected cluster of excluded volume appears with positive probability.Comment: 16 pages, 6 figure

A solidification phenomenon in random packings

Abstract. 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