Ujué Etayo

Random Points on $$\mathbb {S}^3$$ with Small Logarithmic Energy

We analyse several constructions of random point sets on the sphere $\mathbb{S}^{3}\subset\mathbb{R}^4$ evaluating and comparing them through their discrete logarithmic energy: \begin{equation*} E_0(ω_N) = \sum_{\substack{i, j=1\\ i \neq j}}^{N} \log\frac{1}{\|x_i - x_j\|}, \; \t...

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

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 lo...