Approximation to uniform distribution in SO(3)

Damir Ferizović; Carlos Beltrán

doi:10.1007/s00365-020-09506-1

Approximation to uniform distribution in SO(3)

Damir Ferizović, Carlos Beltrán^*

^*Corresponding author for this work

Institute of Analysis and Number Theory (5010)

Research output: Contribution to journal › Article › peer-review

Abstract

Using the theory of determinantal point processes we give upper bounds for the Green and Riesz energies for the rotation group SO (3) , with Riesz parameter up to 3. The Green function is computed explicitly, and a lower bound for the Green energy is established, enabling comparison of uniform point constructions on SO (3). The variance of rotation matrices sampled by a certain determinantal point process is estimated, and formulas for the L ²-norm of Gegenbauer polynomials with index 2 are deduced, which might be of independent interest.

Translated title of the contribution	Approximation der Gleichverteilung in SO(3)
Original language	English
Pages (from-to)	283-311
Number of pages	29
Journal	Constructive Approximation
Volume	52
Issue number	2
Early online date	9 May 2020
DOIs	https://doi.org/10.1007/s00365-020-09506-1
Publication status	Published - 1 Oct 2020

Keywords

Determinantal point processes
Green energy
Point arrangements
Rotation group

ASJC Scopus subject areas

Computational Mathematics
Analysis
Mathematics(all)

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10.1007/s00365-020-09506-1

Cite this

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title = "Approximation to uniform distribution in SO(3)",

abstract = "Using the theory of determinantal point processes we give upper bounds for the Green and Riesz energies for the rotation group SO (3) , with Riesz parameter up to 3. The Green function is computed explicitly, and a lower bound for the Green energy is established, enabling comparison of uniform point constructions on SO (3). The variance of rotation matrices sampled by a certain determinantal point process is estimated, and formulas for the L 2-norm of Gegenbauer polynomials with index 2 are deduced, which might be of independent interest. ",

keywords = "Determinantal point processes, Green energy, Point arrangements, Rotation group",

author = "Damir Ferizovi{\'c} and Carlos Beltr{\'a}n",

year = "2020",

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doi = "10.1007/s00365-020-09506-1",

language = "English",

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pages = "283--311",

journal = "Constructive Approximation",

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T1 - Approximation to uniform distribution in SO(3)

AU - Ferizović, Damir

AU - Beltrán, Carlos

PY - 2020/10/1

Y1 - 2020/10/1

N2 - Using the theory of determinantal point processes we give upper bounds for the Green and Riesz energies for the rotation group SO (3) , with Riesz parameter up to 3. The Green function is computed explicitly, and a lower bound for the Green energy is established, enabling comparison of uniform point constructions on SO (3). The variance of rotation matrices sampled by a certain determinantal point process is estimated, and formulas for the L 2-norm of Gegenbauer polynomials with index 2 are deduced, which might be of independent interest.

AB - Using the theory of determinantal point processes we give upper bounds for the Green and Riesz energies for the rotation group SO (3) , with Riesz parameter up to 3. The Green function is computed explicitly, and a lower bound for the Green energy is established, enabling comparison of uniform point constructions on SO (3). The variance of rotation matrices sampled by a certain determinantal point process is estimated, and formulas for the L 2-norm of Gegenbauer polynomials with index 2 are deduced, which might be of independent interest.

KW - Determinantal point processes

KW - Green energy

KW - Point arrangements

KW - Rotation group

UR - https://arxiv.org/pdf/1901.10840

UR - http://www.scopus.com/inward/record.url?scp=85084515690&partnerID=8YFLogxK

U2 - 10.1007/s00365-020-09506-1

DO - 10.1007/s00365-020-09506-1

M3 - Article

SN - 0176-4276

VL - 52

SP - 283

EP - 311

JO - Constructive Approximation

JF - Constructive Approximation

IS - 2

ER -

Approximation to uniform distribution in SO(3)

Abstract

Keywords

ASJC Scopus subject areas

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Approximation to uniform distribution on SO(3)

Lower Bound of the Discrete Green Energy - Elkies Lemma

An Upper Bound for the Green Energy on SO(3)

Doctoral School Award

Cite this

Approximation to uniform distribution in SO(3)

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Activities

Approximation to uniform distribution on SO(3)

Lower Bound of the Discrete Green Energy - Elkies Lemma

An Upper Bound for the Green Energy on SO(3)

Prizes

Doctoral School Award

Cite this