Density and correlation in a random sequential adsorption model

TL;DR

This paper analyzes a one-dimensional random sequential adsorption model with nearest-neighbor exclusion, providing methods to compute the occupied site density and pair correlation function over time.

Contribution

It introduces a novel approach to calculate density and correlation functions in a 1D RSA model with random site occupation times.

Findings

Derived explicit formulas for site occupation density over time

Calculated pair correlation functions for the model

Provided a computational method for analyzing similar models

Abstract

We consider a random sequential adsorption process on the one-dimensional lattice with nearest-neighbor exclusion. In this model, each site $s \in \mathbb{Z}$ starts empty and we will try to occupy it in time $t_s$, where $(t_s)_{s\in\mathbb{Z}}$ is a sequence of independent random variables uniformly distributed on the interval $[0,1]$. The site will be occupied if both of its neighbors are vacant. We provide a method to calculate the density of occupied sites up to the time $t$, as well as the pair correlation function.