4 papers · 1 filter
Geodesic Distance Riesz Energy on Projective Spaces
Dmitriy Bilyk, Ryan W. Matzke, Joel Nathe
We study probability measures that minimize the Riesz energy with respect to the geodesic distance on projective spaces (such energies arise from…
Riesz and Green energy on projective spaces
Austin Anderson, Maria Dostert, Peter J. Grabner +2
In this paper we study Riesz, Green and logarithmic energy on two-point homogeneous spaces. More precisely we consider the real, the complex, the quaternionic and the Cayley projec…
Positive definiteness and the Stolarsky invariance principle
Dmitriy Bilyk, Ryan Matzke, Oleksandr Vlasiuk
In this paper we elaborate on the interplay between energy optimization, positive definiteness, and discrepancy. In particular, assuming the existence of a -invariant measure $μ…
Energy on spheres and discreteness of minimizing measures
Dmitriy Bilyk, Alexey Glazyrin, Ryan Matzke +2
In the present paper we study the minimization of energy integrals on the sphere with a focus on an interesting clustering phenomenon: for certain types of potentials, optimal meas…