# Likelihood equations and scattering amplitudes

@article{Sturmfels2021LikelihoodEA, title={Likelihood equations and scattering amplitudes}, author={Bernd Sturmfels and Simon Telen}, journal={Algebraic Statistics}, year={2021} }

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…

## 16 Citations

Scattering and Strebel graphs

- MathematicsSciPost Physics
- 2022

We consider a special scattering experiment with n particles in
\mathbb{R}^{1,n-3}ℝ1,n−3.
The scattering equations in this set-up become the saddle-point
equations of a Penner-like matrix model,…

Singularities of eight- and nine-particle amplitudes from cluster algebras and tropical geometry

- MathematicsJournal of High Energy Physics
- 2021

Abstract
We further exploit the relation between tropical Grassmannians and Gr(4, n) cluster algebras in order to make and refine predictions for the singularities of scattering amplitudes in planar…

Maximum Likelihood Estimation from a Tropical and a Bernstein--Sato Perspective

- Mathematics
- 2021

In this article, we investigate Maximum Likelihood Estimation with tools from Tropical Geometry and Bernstein--Sato theory. We investigate the critical points of very affine varieties and study their…

Co-Homology of Differential Forms and Feynman Diagrams

- MathematicsUniverse
- 2021

In the present review we provide an extensive analysis of the intertwinement between Feynman integrals and cohomology theories in light of recent developments. Feynman integrals enter in several…

Notes on worldsheet-like variables for cluster configuration spaces

- Mathematics
- 2021

We continue the exploration of various appearances of cluster algebras in scattering amplitudes and related topics in physics. The cluster configuration spaces generalize the familiar moduli…

Beyond Linear Algebra

- MathematicsArXiv
- 2021

The title challenges the reader to venture beyond linear algebra in designing models and in thinking about numerical algorithms for identifying solutions and the role of nonlinear algebra in the study of linear PDE with constant coefficients.

Toric Geometry of Entropic Regularization

- MathematicsArXiv
- 2022

Entropic regularization is a method for large-scale linear programming. Geometrically, one traces intersections of the feasible polytope with scaled toric varieties, starting at the Birch point. We…

Adjoints and Canonical Forms of Polypols

- Mathematics
- 2021

Polypols are natural generalizations of polytopes, with boundaries given by nonlinear algebraic hypersurfaces. We describe polypols in the plane and in 3-space that admit a unique adjoint…

Marginal Independence Models

- Mathematics, Computer ScienceISSAC
- 2022

The numerical algebra of parameter estimation is developed, using both Euclidean distance and maximum likelihood, and the database of small models is presented, with emphasis on random graph models and independent set polytopes of matroids.

Logarithmic Voronoi polytopes for discrete linear models

- Mathematics
- 2021

We study logarithmic Voronoi cells for linear statistical models and partial linear models. The logarithmic Voronoi cells at points on such model are polytopes. To any d-dimensional linear model…

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