Caging disks and circle disk packings using a generalized ballistic-deposition model

Caging of hard disk, i.e., complete arrest of all translational motions, is realized using a generalized ballistic-deposition model. Analytical solutions for statistical quantities such as the caging probability and the mean number of contact disks are derived. Results are then extended to solve the circle parking problem. Applications to (locally) random disk packings is then discussed.