Determinantal probability measures on Grassmannians
Annales de l’Institut Henri Poincaré D, Tome 9 (2022) no. 4, pp. 659-732.
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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.

Accepté le :
Publié le :
DOI : 10.4171/aihpd/152
Classification : 60-XX, 14-XX, 81-XX, 82-XX
Mots-clés : determinantal measures, geometric probability, integral geometry, random geometry, enumerative geometry, Grassmannians, Plücker coordinates, graded vector spaces, matroid stratification, uniform spanning tree, quantum spanning forest 
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     author = {Kassel, Adrien and L\'evy, Thierry},
     title = {Determinantal probability measures on {Grassmannians}},
     journal = {Annales de l{\textquoteright}Institut Henri Poincar\'e D},
     pages = {659--732},
     volume = {9},
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     year = {2022},
     doi = {10.4171/aihpd/152},
     mrnumber = {4525143},
     zbl = {1511.60072},
     language = {en},
     url = {http://www.numdam.org/articles/10.4171/aihpd/152/}
}
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Kassel, Adrien; Lévy, Thierry. Determinantal probability measures on Grassmannians. Annales de l’Institut Henri Poincaré D, Tome 9 (2022) no. 4, pp. 659-732. doi : 10.4171/aihpd/152. http://www.numdam.org/articles/10.4171/aihpd/152/

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