11 citations · 16 across the 12 of their papers we have counts for
17 papers
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…
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…
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…
Potential theory with multivariate kernels
Dmitriy Bilyk, Damir Ferizović, Alexey Glazyrin +3
In the present paper we develop the theory of minimization for energies with multivariate kernels, i.e. energies, in which pairwise interactions are replaced by interactions betwee…
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…
Optimal measures for p-frame energies on spheres
Dmitriy Bilyk, Alexey Glazyrin, Ryan Matzke +2
We provide new answers about the placement of mass on spheres so as to minimize energies of pairwise interactions. We find optimal measures for the -frame energies, i.e. energie…
The Maximum Size of -Sum-Free Sets in Cyclic Groups
Béla Bajnok, Ryan Matzke
A subset of a finite abelian group is called -sum-free if the sum of (not-necessarily-distinct) elements of never equals the sum of (not-necessarily-dist…
On the Fejes Tóth Problem about the Sum of Angles Between Lines
Dmitriy Bilyk, Ryan W Matzke
In 1959 Fejes Tóth posed a conjecture that the sum of pairwise non-obtuse angles between unit vectors in is maximized by periodically repeated elements of the sta…
Stolarsky principle and energy optimization on the sphere
Dmitriy Bilyk, Feng Dai, Ryan Matzke
The classical Stolarsky invariance principle connects the spherical cap discrepancy of a finite point set on the sphere to the pairwise sum of Euclidean distances between the…
On the Minimum Size of Signed Sumsets in Elementary Abelian Groups
Bela Bajnok, Ryan Matzke
For a finite abelian group and positive integers and , we let and $$ρ_{\pm} (G, m, h) = \min \{|h_{\pm} A| \;…
The Minimum Size of Signed Sumsets
Bela Bajnok, Ryan Matzke
For a finite abelian group and positive integers and , we let and $$ρ_{\pm} (G, m, h) = \min \{|h_{\pm} A| \;…