Linear statistics of determinantal point processes and norm representations
We study the asymptotic behavior of the fluctuations of smooth and rough linear statistics for
determinantal point processes on the sphere and on the Euclidean space. The main tool is …
determinantal point processes on the sphere and on the Euclidean space. The main tool is …
Riesz energy, L 2 L^2 discrepancy, and optimal transport of determinantal point processes on the sphere and the flat torus
B Borda, P Grabner, RW Matzke - Mathematika, 2024 - Wiley Online Library
Determinantal point processes exhibit an inherent repulsive behavior, thus providing
examples of very evenly distributed point sets on manifolds. In this paper, we study the so …
examples of very evenly distributed point sets on manifolds. In this paper, we study the so …
[HTML][HTML] Low-energy points on the sphere and the real projective plane
C Beltrán, U Etayo, PR López-Gómez - Journal of Complexity, 2023 - Elsevier
We present a generalization of a family of points on S 2, the Diamond ensemble, containing
collections of N points on S 2 with very small logarithmic energy for all N∈ N. We extend this …
collections of N points on S 2 with very small logarithmic energy for all N∈ N. We extend this …
Geodesic Distance Riesz Energy on Projective Spaces
D Bilyk, RW Matzke, J Nathe - arXiv preprint arXiv:2409.16508, 2024 - arxiv.org
We study probability measures that minimize the Riesz energy with respect to the geodesic
distance $\vartheta (x, y) $ on projective spaces $\mathbb {FP}^ d $(such energies arise …
distance $\vartheta (x, y) $ on projective spaces $\mathbb {FP}^ d $(such energies arise …
A Lower Bound for the Logarithmic Energy on and for the Green Energy on
C Beltrán, F Lizarte - Constructive Approximation, 2023 - Springer
A Lower Bound for the Logarithmic Energy on $$\mathbb {S}^2$$ and for the Green Energy
on $$\mathbb {S}^n$$ | Constructive Approximation Skip to main content SpringerLink …
on $$\mathbb {S}^n$$ | Constructive Approximation Skip to main content SpringerLink …
Expected energy of zeros of elliptic polynomials
V Torre, J Marzo - Constructive Approximation, 2024 - Springer
Abstract In 2011, Armentano, Beltrán and Shub obtained a closed expression for the
expected logarithmic energy of the random point process on the sphere given by the roots of …
expected logarithmic energy of the random point process on the sphere given by the roots of …
Lower bound for the Green energy of point configurations in harmonic manifolds
C Beltrán, V de la Torre, F Lizarte - Potential Analysis, 2024 - Springer
In this paper, we get the sharpest known to date lower bounds for the minimal Green energy
of the compact harmonic manifolds of any dimension. Our proof generalizes previous ad-hoc …
of the compact harmonic manifolds of any dimension. Our proof generalizes previous ad-hoc …
Carleman estimates for higher step Grushin operators
H De Bie, P Lian - arXiv preprint arXiv:2402.07348, 2024 - arxiv.org
The higher step Grushin operators $\Delta_ {\alpha} $ are a family of sub-elliptic operators
which degenerate on a sub-manifold of $\mathbb {R}^{n+ m} $. This paper establishes …
which degenerate on a sub-manifold of $\mathbb {R}^{n+ m} $. This paper establishes …
Minimal Riesz and logarithmic energies on the Grassmannian
U Etayo, PR López-Gómez - arXiv preprint arXiv:2501.00424, 2024 - arxiv.org
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 …
{2, 4} $ of $2 $-dimensional subspaces of $\mathbb {R}^ 4$. We prove that the continuous …
Hyperuniform point sets on projective spaces
JS Brauchart, PJ Grabner - arXiv preprint arXiv:2403.03572, 2024 - arxiv.org
We extend the notion of hyperuniformity to the projective spaces $\mathbb {RP}^{d-1} $,
$\mathbb {CP}^{d-1} $, $\mathbb {HP}^{d-1} $, and $\mathbb {OP}^ 2$. We show that …
$\mathbb {CP}^{d-1} $, $\mathbb {HP}^{d-1} $, and $\mathbb {OP}^ 2$. We show that …