Dynamic Space Packing

TL;DR

This paper introduces and solves a dynamic space packing model, analyzing its steady-state properties and correlations for both lattice and continuous spaces, revealing new solvable stochastic processes.

Contribution

It provides the first exact solutions for the steady-state and statistical features of dynamic space packing in both lattice and continuous settings.

Findings

Steady-state occupancy and correlation functions are explicitly derived.

The model's desorption probabilities are characterized.

Exact solutions are obtained for both lattice and continuous DSP models.

Abstract

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 $\mathbb{R}^d$.