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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
70/2017

The Geometry of Gaussoids

Tobias Boege, Alessio D'Ali, Thomas Kahle and Bernd Sturmfels

Abstract

A gaussoid is a combinatorial structure that encodes independence in probability and statistics, just like matroids encode independence in linear algebra. The gaussoid axioms of Lnenicka and Matus are equivalent to compatibility with certain quadratic relations among principal and almost-principal minors of a symmetric matrix. We develop the geometric theory of gaussoids, based on the Lagrangian Grassmannian and its symmetries. We introduce oriented gaussoids and valuated gaussoids, thus connecting to real and tropical geometry. We classify small realizable and non-realizable gaussoids. Positive gaussoids are as nice as positroids: they are all realizable via graphical models.

Received:
20.10.17
Published:
20.10.17

Related publications

inJournal
2019 Repository Open Access
Tobias Boege, Alessio D'Alì, Thomas Kahle and Bernd Sturmfels

The geometry of Gaussoids

In: Foundations of computational mathematics, 19 (2019) 4, pp. 775-812