# Occupancy correlations in the asymmetric simple inclusion process

## TL;DR

This paper derives an exact formula for occupancy correlations in the asymmetric simple inclusion process, enhancing understanding of joint occupancy distributions in this unidirectional transport model.

## Contribution

It provides the first analytical expression for the covariance matrix of steady-state occupancy, bridging a gap in understanding the model's joint distribution.

## Key findings

- Derived an exact covariance matrix formula for ASIP occupancy.
- Validated the formula through Monte-Carlo simulations.
- Mapped spatial occupancy correlations in arbitrary-sized systems.

## Abstract

The asymmetric simple inclusion process (ASIP) --- a lattice-gas model for unidirectional transport with irreversible aggregation --- has been proposed as an inclusion counterpart of the asymmetric simple exclusion process and as a batch service counterpart of the tandem Jackson network. To date, analytical tractability of the model has been limited: while the average particle density in the model is easy to compute, very little is known about its joint occupancy distribution. To partially bridge this gap, we study occupancy correlations in the ASIP. We take an analytical approach to this problem and derive an exact formula for the covariance matrix of the steady-state occupancy vector. We verify the validity of this formula numerically in small ASIP systems, where Monte-Carlo simulations can provide reliable estimates for correlations in reasonable time, and further use it to draw a comprehensive picture of spatial occupancy correlations in ASIP systems of arbitrary size.