On the mean projection theorem for determinantal point processes

TL;DR

This paper extends a mean projection theorem from discrete to continuous determinantal point processes, providing new formulas for variance and strengthening existing results in random linear algebra.

Contribution

It generalizes a known discrete theorem to continuous cases and introduces a new variance formula for the exterior power of the random projection.

Findings

Extended the mean projection theorem to continuous determinantal point processes.

Provided a new formula for the variance of the exterior power of the random projection.

Strengthened the connection between determinantal point processes and random linear algebra.

Abstract

In this short note, we extend to the continuous case a mean projection theorem for discrete determinantal point processes associated with a finite range projection, thus strengthening a known result in random linear algebra due to Ermakov and Zolotukhin. We also give a new formula for the variance of the exterior power of the random projection.