Abstract
AbstractGibbs manifolds are images of affine spaces of symmetric matrices under the exponential map. They arise in applications such as optimization, statistics and quantum physics, where they extend the ubiquitous role of toric geometry. The Gibbs variety is the zero locus of all polynomials that vanish on the Gibbs manifold. We compute these polynomials and show that the Gibbs variety is low-dimensional. Our theory is applied to a wide range of scenarios, including matrix pencils and quantum optimal transport.
Funder
Nederlandse Organisatie voor Wetenschappelijk Onderzoek
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Theory and Mathematics,Computer Science Applications,Geometry and Topology,Statistics and Probability
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