1. Introduction to the model
In this paper will be a positive semi-definite matrix. Let , . We call a random subset of a determinantal point process if the following holds
and by definition . (Where .)
Basically, we have a set of points, and we pick a random subset
of them. We model the probability that all the points in the subsetwere chosen by .
Instead of modeling with the kernel , in practice a determinantal point process is modeled as an -ensemble. The process is called the -ensemble with the kernel if
where is a positive semi-definite matrix.
An -ensemble with kernel is a DPP with the kernel