# A note related to the CS decomposition and the BK inequality for discrete determinantal processes

## TL;DR

This paper establishes that the BK inequality holds for increasing events in discrete determinantal processes and explores their relationship with the CS decomposition, providing new insights into their structure.

## Contribution

It introduces a proof of the BK inequality for discrete determinantal processes and links these processes to the CS decomposition, offering novel theoretical connections.

## Key findings

- BK inequality holds for increasing events in discrete determinantal processes
- Established a relationship between determinantal processes and the CS decomposition
- Provided elementary insights into the structure of these processes

## Abstract

We prove that for a discrete determinantal process the BK inequality occurs for increasing events generated by simple points. We give also some elementary, but nonetheless appealing relationship, between a discrete determinantal process and the well-known CS decomposition.