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A note related to the CS decomposition and the BK inequality for discrete determinantal processes

Part of: Basic linear algebra Stochastic processes Special processes

Published online by Cambridge University Press:  24 October 2022

André Goldman
André Goldman*
Affiliation:
University Claude Bernard Lyon 1
*
*Postal address: Institut Camille Jordan UMR 5208, Université Claude Bernard Lyon 1, 43 boulevard du 11 novembre 1918 F-69622 Villeurbanne Cedex. Email: andre.goldman@univ-lyon1.fr
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Abstract

We prove that for a discrete determinantal process the BK inequality occurs for increasing events generated by simple points. We also give some elementary but nonetheless appealing relationships between a discrete determinantal process and the well-known CS decomposition.

Keywords

Point processesnegative dependencespanning treesexterior algebraprincipal angles

MSC classification

Primary: 60K99: None of the above, but in this section 60G55: Point processes 15A23: Factorization of matrices
Secondary: 68U99: None of the above, but in this section 15A75: Exterior algebra, Grassmann algebras
Type
Original Article
Information
Journal of Applied Probability , Volume 60 , Issue 1 , March 2023 , pp. 189 - 203
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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