Tree representations of $ \alpha$-determinantal point processes

TL;DR

This paper extends the tree representation method from determinantal point processes to the more general $\alpha$-determinantal point processes, providing a new analytical tool for this class of stochastic models.

Contribution

It introduces and proves the applicability of tree representations to $\alpha$-determinantal point processes, expanding the analytical framework beyond determinantal processes.

Findings

Tree representation applies to $\alpha$-determinantal processes

Generalization from determinantal to $\alpha$-determinantal processes

Provides new analytical tools for $\alpha$-determinantal processes

Abstract

We introduce tree representations for $ \alpha$-determinantal point processes. The $ \alpha$-determinantal point processes is introduced as a one parameter extension of the determinantal point process. In the previous paper with H.Osada, the tree representation was introduced for determinantal point processes. In this paper, we prove that the tree representation can be applied to $ \alpha$-determinantal point processes.