# A Model for Random Chain Complexes

## TL;DR

This paper introduces a probabilistic model for chain complexes over finite fields, analyzing their combinatorial and homological properties when boundary maps are randomly generated.

## Contribution

It presents a novel model for random chain complexes over finite fields, with a detailed study of their structural and homological characteristics.

## Key findings

- Characterization of the distribution of homology groups
- Analysis of the typical ranks of boundary maps
- Insights into the probabilistic structure of chain complex properties

## Abstract

We introduce a model for random chain complexes over a finite field. The randomness in our complex comes from choosing the entries in the matrices that represent the boundary maps uniformly over $\mathbb{F}_q$, conditioned on ensuring that the composition of consecutive boundary maps is the zero map. We then investigate the combinatorial and homological properties of this random chain complex.