Topology of the Nodal Set of Random Equivariant Spherical Harmonics on 3

Junehyuk Jung; Steve Zelditch

doi:10.1093/imrn/rnz348

Topology of the Nodal Set of Random Equivariant Spherical Harmonics on ³

Junehyuk Jung^*, Steve Zelditch

^*Corresponding author for this work

Mathematics

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

2 Scopus citations

Abstract

We show that real and imaginary parts of equivariant spherical harmonics on S3 have almost surely a single nodal component. Moreover, if the degree of the spherical harmonic is N and the equivariance degree is m, then the expected genus is proportional to m (N2 - m22 + N). Hence, if mN= c for fixed 0 < c < 1, then the genus has order N³.

Original language	English (US)
Pages (from-to)	8521-8549
Number of pages	29
Journal	International Mathematics Research Notices
Volume	2021
Issue number	11
DOIs	https://doi.org/10.1093/imrn/rnz348
State	Published - Jun 1 2021

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1093/imrn/rnz348

Cite this

@article{a7bde21c3b1941c2a42c3a83160aca88,

title = "Topology of the Nodal Set of Random Equivariant Spherical Harmonics on 3",

abstract = "We show that real and imaginary parts of equivariant spherical harmonics on S3 have almost surely a single nodal component. Moreover, if the degree of the spherical harmonic is N and the equivariance degree is m, then the expected genus is proportional to m (N2 - m22 + N). Hence, if mN= c for fixed 0 < c < 1, then the genus has order N3.",

author = "Junehyuk Jung and Steve Zelditch",

year = "2021",

month = jun,

day = "1",

doi = "10.1093/imrn/rnz348",

language = "English (US)",

volume = "2021",

pages = "8521--8549",

journal = "International Mathematics Research Notices",

issn = "1073-7928",

publisher = "Oxford University Press",

number = "11",

}

TY - JOUR

T1 - Topology of the Nodal Set of Random Equivariant Spherical Harmonics on 3

AU - Jung, Junehyuk

AU - Zelditch, Steve

PY - 2021/6/1

Y1 - 2021/6/1

N2 - We show that real and imaginary parts of equivariant spherical harmonics on S3 have almost surely a single nodal component. Moreover, if the degree of the spherical harmonic is N and the equivariance degree is m, then the expected genus is proportional to m (N2 - m22 + N). Hence, if mN= c for fixed 0 < c < 1, then the genus has order N3.

AB - We show that real and imaginary parts of equivariant spherical harmonics on S3 have almost surely a single nodal component. Moreover, if the degree of the spherical harmonic is N and the equivariance degree is m, then the expected genus is proportional to m (N2 - m22 + N). Hence, if mN= c for fixed 0 < c < 1, then the genus has order N3.

UR - http://www.scopus.com/inward/record.url?scp=85126621474&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85126621474&partnerID=8YFLogxK

U2 - 10.1093/imrn/rnz348

DO - 10.1093/imrn/rnz348

M3 - Article

AN - SCOPUS:85126621474

SN - 1073-7928

VL - 2021

SP - 8521

EP - 8549

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

IS - 11

ER -

Topology of the Nodal Set of Random Equivariant Spherical Harmonics on ³

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this