  Dynamic space packing (DSP) is a random process with sequential addition and
removal of identical objects into space. In the lattice version, objects are
particles occupying single lattice sites, and adding a particle to a lattice
site leads to the removal of particles on neighboring sites. We show that the
model is solvable and determine the steady-state occupancy, correlation
functions, desorption probabilities, and other statistical features for the DSP
of hyper-cubic lattices. We also solve a continuous DSP of balls into
$\mathbb{R}^d$.

Statistical Mechanics;Disordered Systems and Neural Networks;Probability