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Likelihood
equations and scattering amplitudes
Bernd Sturmfels and Simon Telen |
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Vol. 12 (2021), No. 2, 167–186
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DOI: 10.2140/astat.2021.12.167
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Abstract |
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We relate scattering amplitudes in particle physics to maximum likelihood estimation for discrete models in algebraic statistics. The scattering potential plays the role of the log-likelihood function, and its critical points are solutions to rational function equations. We study the ML degree of low-rank tensor models in statistics, and we revisit physical theories proposed by Arkani-Hamed, Cachazo and their collaborators. Recent advances in numerical algebraic geometry are employed to compute and certify critical points. We also discuss positive models and how to compute their amplitudes. |
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Keywords
likelihood equations, scattering amplitudes, numerical
nonlinear algebra
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Mathematical Subject Classification
Primary: 62R01, 65H14
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Milestones
Received: 9 December 2020
Revised: 29 April 2021
Accepted: 18 May 2021
Published: 13 December 2021
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Authors |
| Bernd Sturmfels | |
| Max Planck Institute for Mathematics
in the Sciences Leipzig Germany |
Department of Mathematics University of California, Berkeley Berkeley, CA United States |
| Simon Telen | |
| Max Planck Institute for Mathematics
in the Sciences Leipzig Germany |
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