# Fluctuations of the partial filling factors in competitive RSA from binary mixtures

## TL;DR

This paper investigates the fluctuations in partial filling factors during competitive RSA of binary particles on a line, revealing strong correlations and size-dependent variance behaviors through analytic and simulation methods.

## Contribution

It introduces an analytic recursive approach combined with Monte Carlo simulations to analyze fluctuations and correlations in binary RSA, highlighting size ratio effects.

## Key findings

- Total fill factor fluctuations are small despite large partial fluctuations.
- Larger particles exhibit more correlated distribution fluctuations.
- Variance in smaller particle contribution is influenced by gap size fluctuations.

## Abstract

Competitive random sequential adsorption on a line from a binary mix of incident particles is studied using both an analytic recursive approach and Monte Carlo simulations. We find a strong correlation between the small and the large particle distributions so that while both partial contributions to the fill factor fluctuate widely, the variance of the total fill factor remains relatively small. The variances of partial contributions themselves are quite different between the smaller and the larger particles, with the larger particle distribution being more correlated. The disparity in fluctuations of partial fill factors increases with the particle size ratio. The additional variance in the partial contribution of smaller particle originates from the fluctuations in the size of gaps between larger particles. We discuss the implications of our results to semiconductor high-energy gamma detectors where the detector energy resolution is controlled by correlations in the cascade energy branching process.