Complete quadrics: Schubert calculus for Gaussian models and semidefinite programming

IF 2.5 1区 数学 Q1 MATHEMATICS Journal of the European Mathematical Society Pub Date : 2020-11-17 DOI:10.4171/jems/1330
L. Manivel, M. Michałek, Leonid Monin, Tim Seynnaeve, Martin Vodivcka
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引用次数: 22

Abstract

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.
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完全二次:舒伯特演算高斯模型和半定规划
我们建立了线性集中模型的最大似然度(ml度)、半定规划的代数度(SDP)和完全二次曲线的Schubert微积分之间的联系。我们证明了sturmfeles和Uhler关于ml度的多项式性的一个猜想。我们还证明了Nie, Ranestad和Sturmfels的猜想,提供了SDP程度的显式公式。这三个场之间的相互作用揭示了各种完全二次型的枚举不变量的渐近行为。我们也将这些结果推广到一般矩阵和偏对称矩阵的空间。
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来源期刊
CiteScore
4.50
自引率
0.00%
发文量
103
审稿时长
6-12 weeks
期刊介绍: The Journal of the European Mathematical Society (JEMS) is the official journal of the EMS. The Society, founded in 1990, works at promoting joint scientific efforts between the many different structures that characterize European mathematics. JEMS will publish research articles in all active areas of pure and applied mathematics. These will be selected by a distinguished, international board of editors for their outstanding quality and interest, according to the highest international standards. Occasionally, substantial survey papers on topics of exceptional interest will also be published. Starting in 1999, the Journal was published by Springer-Verlag until the end of 2003. Since 2004 it is published by the EMS Publishing House. The first Editor-in-Chief of the Journal was J. Jost, succeeded by H. Brezis in 2004. The Journal of the European Mathematical Society is covered in: Mathematical Reviews (MR), Current Mathematical Publications (CMP), MathSciNet, Zentralblatt für Mathematik, Zentralblatt MATH Database, Science Citation Index (SCI), Science Citation Index Expanded (SCIE), CompuMath Citation Index (CMCI), Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), ISI Alerting Services, Journal Citation Reports/Science Edition, Web of Science.
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