Work

Minimal Riesz and logarithmic energies on the Grassmannian $\operatorname{Gr}_{2,4}$

Year: 2026

Type: article

Abstract: We study the Riesz and logarithmic energies on the Grassmannian \operatorname{Gr}_{2,4} of 2 -dimensional subspaces of \mathbb{R}^{4} . We prove that the continuous Riesz and logarithmic energies are uniquely minimized by the uniform measure, and we obtain asymptotic upper and lower bounds for the minimal discrete energies, with matching orders for the next-order terms. Additionally, we define a determinantal point process on \operatorname{Gr}_{2,4} and compute the expected energy of the points coming from this random process, thereby obtaining explicit constants in the upper bounds for the Riesz and logarithmic energies.

Source: Revista Matemática Iberoamericana

DOI: 10.4171/rmi/1645

Authors: Ujué Etayo, Pedro R. López-Gómez

Institution: CUNEF Universidad

Language: English

Topic: Mathematical Approximation and Integration

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Fundación BBVA, Agencia Estatal de Investigación, European Social Fund