Determinantal point processes and fermionic Fock space

TL;DR

This paper establishes a mathematical connection between determinantal point processes and fermionic Fock space by constructing an explicit embedding and spectral measure, advancing the theoretical understanding of these structures.

Contribution

It introduces a canonical embedding of $L^2$ over a determinantal process into fermionic Fock space and identifies the process as a spectral measure for Gaussian operators.

Findings

Constructed a canonical embedding of $L^2$ into fermionic Fock space.

Demonstrated that a determinantal process is the spectral measure for Gaussian operators.

Provided explicit mathematical framework linking determinantal processes and fermionic Fock space.

Abstract

We construct a canonical embedding of the space $L^2$ over a determinantal point process to the fermionic Fock space. Equivalently, we show that a determinantal process is the spectral measure for some explicit commutative group of Gaussian operators in the fermionic Fock space.