Zobrazeno 1 - 10
of 34
pro vyhledávání: '"Vlasiuk, Oleksandr"'
Autor:
Bilyk, Dmitriy, Ferizović, Damir, Glazyrin, Alexey, Matzke, Ryan W., Park, Josiah, Vlasiuk, Oleksandr
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 points, which serve as multi-input generalizations of the well-known Ri
Externí odkaz:
http://arxiv.org/abs/2303.14258
Autor:
Bilyk, Dmitriy, Ferizović, Damir, Glazyrin, Alexey, Matzke, Ryan, Park, Josiah, Vlasiuk, Oleksandr
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 distances between points to the context of three-point potentials. In
Externí odkaz:
http://arxiv.org/abs/2303.12283
We obtain new asymptotic results about systems of $ N $ particles governed by Riesz interactions involving $ k $-nearest neighbors of each particle as $N\to\infty$. These results include a generalization to weighted Riesz potentials with external fie
Externí odkaz:
http://arxiv.org/abs/2201.00474
In this paper we elaborate on the interplay between energy optimization, positive definiteness, and discrepancy. In particular, assuming the existence of a $K$-invariant measure $\mu$ with full support, we show that conditional positive definiteness
Externí odkaz:
http://arxiv.org/abs/2110.04138
Autor:
Bilyk, Dmitriy, Ferizović, Damir, Glazyrin, Alexey, Matzke, Ryan, Park, Josiah, Vlasiuk, Oleksandr
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 between triples or, more generally, $n$-tuples of particles. Such objects, w
Externí odkaz:
http://arxiv.org/abs/2104.03410
We describe a framework for extending the asymptotic behavior of a short-range interaction from the unit cube to general compact subsets of $ \mathbb R^d $. This framework allows us to give a unified treatment of asymptotics of hypersingular Riesz en
Externí odkaz:
http://arxiv.org/abs/2010.11937
Autor:
Vlasiuk, Oleksandr
It is shown that the supports of measures minimizing weakly repulsive energies on Riemannian manifolds with sectional curvature bounded below do not have concentration points. This extends the results of Bj\"orck and Carrillo, Figalli, and Patacchini
Externí odkaz:
http://arxiv.org/abs/2003.01597
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 measures are discrete or are supported on small sets. In particular, we pr
Externí odkaz:
http://arxiv.org/abs/1908.10354
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 $p$-frame energies, i.e. energies with the kernel given by the absolute value of the inner product rai
Externí odkaz:
http://arxiv.org/abs/1908.00885
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