Topology of the Nodal Set of Random Equivariant Spherical Harmonics on 𝕊3
| Autor: | Steve Zelditch, Junehyuk Jung |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Mathematics - Differential Geometry
Degree (graph theory) General Mathematics Probability (math.PR) Spherical harmonics Order (ring theory) Topology (electrical circuits) Mathematics - Spectral Theory Combinatorics Mathematics::Algebraic Geometry Differential Geometry (math.DG) Genus (mathematics) FOS: Mathematics Equivariant map Component (group theory) Almost surely Spectral Theory (math.SP) Mathematics - Probability Mathematics |
| Zdroj: | International Mathematics Research Notices. 2021:8521-8549 |
| ISSN: | 1687-0247 1073-7928 |
| DOI: | 10.1093/imrn/rnz348 |
| Popis: | We show that real and imaginary parts of equivariant spherical harmonics on $S^3$ 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 \left(\frac{N^2 - m^2}{2} + N\right) $. Hence if $\frac{m}{N}= c $ for fixed $0 < c < 1$, the genus has order $N^3$. 15 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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