Determinantal probability measures on Grassmannians

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.

55 pages, 2 figures

References in corpus (2)

• Combinatorial Quantum Field Theory and Gluing Formula for Determinants
• Determinantal point processes and fermion quasifree states

Cited by in corpus (4)

• Asymptotics of the determinant of discrete Laplacians on triangulated and quadrangulated surfaces
• Pfaffian Point Processes from Free Fermion Algebras: Perfectness and Conditional Measures
• On the mean projection theorem for determinantal point processes
• On sampling determinantal and Pfaffian point processes on a quantum computer