On negative association of some finite point processes on general state spaces, extended version

TL;DR

This paper investigates negative association in mixed sampled point processes, establishing conditions under which it holds, and explores its implications for dependence ordering and specific process classes like determinantal processes.

Contribution

It introduces conditions based on ULC property for negative association in mixed sampled point processes and links NA with dcx dependence ordering.

Findings

NA holds for processes with ULC property

Connections between NA and dcx dependence ordering established

Applications demonstrate the theory's relevance

Abstract

We study negative association (NA) for mixed sampled point processes and show that NA holds for such processes if the random number of points of them fulfills ULC property. We connect NA property of point processes with dcx dependence ordering and show some consequences of it for mixed sampled and determinantal point processes. Some applications illustrate general theory.