The Projective Ensemble and Distribution of Points in Odd-Dimensional Spheres

被引：13

作者：

Beltran, Carlos ^{[1
]}

Etayo, Ujue ^{[1
]}

机构：

[1] Univ Cantabria, Dept Matemat Estadist & Comp, Fac Ciencias, Avd Los Castros S-N, E-39005 Santander, Spain

来源：

CONSTRUCTIVE APPROXIMATION | 2018年 / 48卷 / 01期

关键词：

Determinantal point processes; Minimal Riesz energy; Minimal Green energy; MINIMAL DISCRETE ENERGY; ASYMPTOTIC-EXPANSION; RENORMALIZED ENERGY; RIESZ ENERGY;

D O I：

10.1007/s00365-018-9426-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a determinantal point process on the complex projective space that reduces to the so-called spherical ensemble for complex dimension 1 under identification of the 2-sphere with the Riemann sphere. Through this determinantal point process, we propose a new point processs in odd-dimensional spheres that produces fairly well-distributed points, in the sense that the expected value of the Riesz 2-energy for these collections of points is smaller than all previously known bounds.

引用

页码：163 / 182

页数：20

共 20 条

[1] The spherical ensemble and uniform distribution of points on the sphere
Alishahi, Kasra
Zamani, Mohammadsadegh
[J]. ELECTRONIC JOURNAL OF PROBABILITY, 2015, 20 : 1 - 27
[2] Beltran C., ARXIV170200864MATHDG
[3] Energy and discrepancy of rotationally invariant determinantal point processes in high dimensional spheres
Beltran, Carlos
Marzo, Jordi
Ortega-Cerda, Joaquim
[J]. JOURNAL OF COMPLEXITY, 2016, 37 : 76 - 109
[4] Determinantal Point Processes and Fermions on Complex Manifolds: Large Deviations and Bosonization
Berman, Robert J.
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2014, 327 (01) : 1 - 47
[5] Renormalized Energy and Asymptotic Expansion of Optimal Logarithmic Energy on the Sphere
Betermin, Laurent
Sandier, Etienne
[J]. CONSTRUCTIVE APPROXIMATION, 2018, 47 (01) : 39 - 74
[6] Borodachov S., MINIMAL DISCRETE ENE
[7] The next-order term for optimal Riesz and logarithmic energy asymptotics on the sphere
Brauchart, J. S.
Hardin, D. P.
Saff, E. B.
[J]. RECENT ADVANCES IN ORTHOGONAL POLYNOMIALS, SPECIAL FUNCTIONS, AND THEIR APPLICATIONS, 2011, 578 : 31 - +
[8] The Riesz energy of the Nth roots of unity: an asymptotic expansion for large N
Brauchart, J. S.
Hardin, D. P.
Saff, E. B.
[J]. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2009, 41 : 621 - 633
[9] About the second term of the asymptotics for optimal Riesz energy on the sphere in the potential-theoretical case
Brauchart, Johann S.
[J]. INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2006, 17 (05) : 321 - 328
[10] Distributing many points on spheres: Minimal energy and designs
Brauchart, Johann S.
Grabner, Peter J.
[J]. JOURNAL OF COMPLEXITY, 2015, 31 (03) : 293 - 326

← 1 2 →