The exact probability distribution of saturating states in random sequential adsorption

TL;DR

This paper derives the exact probability distribution of saturating states in a one-dimensional random sequential adsorption process, providing a new state representation that simplifies the calculation.

Contribution

It introduces a novel state representation for RSA, enabling exact analytical calculation of saturating state probabilities in one dimension.

Findings

Exact probability distribution of saturating states obtained

New state representation simplifies RSA calculations

Analytical results enhance understanding of RSA processes

Abstract

We consider the non-overlapping irreversible random sequential adsorption (RSA) process on one-dimensional finite line, which is known also as the car parking process. The probability of each coverage in saturating states is analytically and exactly obtained. In the derivation, a new representation of states in RSA process is introduced, which effectively works to make the calculation clear and simple.