Determinantal probability measures on Grassmannians

Adrien Kassel (1) , Thierry Levy (2)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées
2 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation

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.

Domaines: Probabilités [math.PR]; Combinatoire [math.CO]; Physique mathématique [math-ph]

Adrien Kassel, Thierry Levy. Determinantal probability measures on Grassmannians. Annales de l’Institut Henri Poincaré (D) Combinatorics, Physics and their Interactions, 2022, 9 (4), pp.659-732. ⟨10.4171/AIHPD/152⟩. ⟨hal-02333790v2⟩