Determinantal probability measures on Grassmannians

TL;DR

This paper introduces a new class of determinantal probability measures on Grassmannians, extending discrete determinantal point processes to continuous settings with symmetry properties.

Contribution

It generalizes determinantal point processes to measures on Grassmannians, characterized by positive self-adjoint contractions and symmetry under isometry groups.

Findings

Defines a new class of determinantal measures on Grassmannians

Establishes properties and invariance under isometry groups

Connects measures to positive self-adjoint contractions

Abstract

We introduce and study a class of determinantal probability measures generalising the class of discrete determinantal point processes. These measures live on the Grassmannian of a real, complex, or quaternionic inner product space that is split into pairwise orthogonal finite-dimensional subspaces. They are determined by a positive self-adjoint contraction of the inner product space, in a way that is equivariant under the action of the group of isometries that preserve the splitting.