11 citations · 16 across the 12 of their papers we have counts for
6 papers · 1 filter
A random line intersects in two probabilistically independent locations
Dmitriy Bilyk, Alan Chang, Otte Heinävaara +2
We consider random lines in (random with respect to the kinematic measure) and how they intersect . It is known that the entry point and the exit point…
Riesz Energy, Discrepancy, and Optimal Transport of Determinantal Point Processes on the Sphere and the Flat Torus
Bence Borda, Peter Grabner, Ryan W. Matzke
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-cal…
Minimizers for an aggregation model with attractive-repulsive interaction
Rupert L. Frank, Ryan W. Matzke
We solve explicitly a certain minimization problem for probability measures involving an interaction energy that is repulsive at short distances and attractive at large distances.…
Optimal Measures for Multivariate Geometric Potentials
Dmitriy Bilyk, Damir Ferizović, Alexey Glazyrin +3
We study measures and point configurations optimizing energies based on multivariate potentials. The emphasis is put on potentials defined by geometric characteristics of sets of p…
Optimizers of three-point energies and nearly orthogonal sets
Dmitriy Bilyk, Damir Ferizović, Alexey Glazyrin +3
This paper is devoted to spherical measures and point configurations optimizing three-point energies. Our main goal is to extend the classic optimization problems based on pairs of…
Polarization and Greedy Energy on the Sphere
Dmitriy Bilyk, Michelle Mastrianni, Ryan W. Matzke +1
We investigate the behavior of a greedy sequence on the sphere defined so that at each step the point that minimizes the Riesz -energy is added to the existing se…