Exponential varieties. Issue 1 (7th January 2016)

• Record Type: Journal Article
• Authors: Michałek, Mateusz; Sturmfels, Bernd; Uhler, Caroline; Zwiernik, Piotr
• Is Part Of: Proceedings of the London Mathematical Society. Volume 112:Issue 1(2016:Jan.)
• Page Start: 27
• Page End: 56
• Publication Date: 2016-01-07
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1112/plms/pdv066
• Languages: English
• ISSNs: 0024-6115

Abstract

Abstract : Exponential varieties arise from exponential families in statistics. These real algebraic varieties have strong positivity and convexity properties, familiar from toric varieties and their moment maps. Among them are varieties of inverses of symmetric matrices satisfying linear constraints. This class includes Gaussian graphical models. We develop a general theory of exponential varieties. These are derived from hyperbolic polynomials and their integral representations. We compare the multidegrees and ML degrees of the gradient map for hyperbolic polynomials.