## 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 subset

were 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.

###### Theorem 1.

An -ensemble with kernel is a DPP with the kernel

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