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Exponential varieties

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2016

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Sturmfels, Bernd
Uhler, Caroline
Zwiernik, Piotr

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https://doi.org/10.1112/plms/pdv066
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http://arxiv.org/abs/1412.6185v2

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Proceedings of the London Mathematical Society. Wiley-Blackwell. 2016, 112(1), pp. 27-56. ISSN 0024-6115. eISSN 1460-244X. Available under: doi: 10.1112/plms/pdv066

Zusammenfassung

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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510 Mathematik

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ISO 690MICHALEK, Mateusz, Bernd STURMFELS, Caroline UHLER, Piotr ZWIERNIK, 2016. Exponential varieties. In: Proceedings of the London Mathematical Society. Wiley-Blackwell. 2016, 112(1), pp. 27-56. ISSN 0024-6115. eISSN 1460-244X. Available under: doi: 10.1112/plms/pdv066
BibTex
@article{Michalek2016Expon-52350,
  year={2016},
  doi={10.1112/plms/pdv066},
  title={Exponential varieties},
  number={1},
  volume={112},
  issn={0024-6115},
  journal={Proceedings of the London Mathematical Society},
  pages={27--56},
  author={Michalek, Mateusz and Sturmfels, Bernd and Uhler, Caroline and Zwiernik, Piotr}
}
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