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Exponential Varieties

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arxiv 1412.6185 v2 pith:LKDNGMQJ submitted 2014-12-18 math.AG math.STstat.TH

Mateusz Micha{l}ek , Bernd Sturmfels , Caroline Uhler , Piotr Zwiernik This is my paper
classification math.AGmath.STstat.TH
keywords varietiesexponentialhyperbolicpolynomialsalgebraicariseclasscompare
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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.

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