Determinantal probability measures on Grassmannians

  • Adrien Kassel

    École Normale Supérieure de Lyon, France
  • Thierry Lévy

    Sorbonne Université, Paris, France
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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.

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Adrien Kassel, Thierry Lévy, Determinantal probability measures on Grassmannians. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 9 (2022), no. 4, pp. 659–732

DOI 10.4171/AIHPD/152