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Complete quadrics : Schubert calculus for Gaussian models and semidefinite programming

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2023

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Manivel, Laurent
Monin, Leonid
Seynnaeve, Tim

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Journal of the European Mathematical Society. EMS Press. 2023, 26(8), S. 3091-3135. ISSN 1435-9855. eISSN 1435-9863. Verfügbar unter: doi: 10.4171/jems/1330

Zusammenfassung

We establish connections between the maximum likelihood degree (ML-degree) for linear concentration models, the algebraic degree of semidefinite programming (SDP), and Schubert calculus for complete quadrics. We prove a conjecture by Sturmfels and Uhler on the polynomiality of the ML-degree. We also prove a conjecture by Nie, Ranestad and Sturmfels providing an explicit formula for the degree of SDP. The interactions between the three fields shed new light on the asymptotic behaviour of enumerative invariants for the variety of complete quadrics. We also extend these results to spaces of general matrices and of skew-symmetric matrices.

Zusammenfassung in einer weiteren Sprache

Fachgebiet (DDC)
510 Mathematik

Schlagwörter

Complete quadrics Lascoux coefficients, ML-degree, SDP-degree, Lascoux polynomials

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ISO 690MANIVEL, Laurent, Mateusz MICHALEK, Leonid MONIN, Tim SEYNNAEVE, Martin VODICKA, 2023. Complete quadrics : Schubert calculus for Gaussian models and semidefinite programming. In: Journal of the European Mathematical Society. EMS Press. 2023, 26(8), S. 3091-3135. ISSN 1435-9855. eISSN 1435-9863. Verfügbar unter: doi: 10.4171/jems/1330
BibTex
@article{Manivel2023-05-03Compl-70261,
  year={2023},
  doi={10.4171/jems/1330},
  title={Complete quadrics : Schubert calculus for Gaussian models and semidefinite programming},
  number={8},
  volume={26},
  issn={1435-9855},
  journal={Journal of the European Mathematical Society},
  pages={3091--3135},
  author={Manivel, Laurent and Michalek, Mateusz and Monin, Leonid and Seynnaeve, Tim and Vodicka, Martin}
}
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