Fluctuations in the number of nodal domains
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2020
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911639003987968 |
|---|---|
| author | Nazarov, Fedor Sodin, Mikhail |
| author_facet | Nazarov, Fedor Sodin, Mikhail |
| contents | We show that the variance of the number of connected components of the zero set of the two-dimensional Gaussian ensemble of random spherical harmonics of degree n grows as a positive power of n. The proof uses no special properties of spherical harmonics and works for any sufficiently regular ensemble of Gaussian random functions on the two-dimensional sphere with distribution invariant with respect to isometries of the sphere.
Our argument connects the fluctuations in the number of nodal lines with those in a random loop ensemble on planar graphs of degree four, which can be viewed as a step towards justification of the Bogomolny-Schmit heuristics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2006_07730 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Fluctuations in the number of nodal domains Nazarov, Fedor Sodin, Mikhail Probability Mathematical Physics Classical Analysis and ODEs We show that the variance of the number of connected components of the zero set of the two-dimensional Gaussian ensemble of random spherical harmonics of degree n grows as a positive power of n. The proof uses no special properties of spherical harmonics and works for any sufficiently regular ensemble of Gaussian random functions on the two-dimensional sphere with distribution invariant with respect to isometries of the sphere. Our argument connects the fluctuations in the number of nodal lines with those in a random loop ensemble on planar graphs of degree four, which can be viewed as a step towards justification of the Bogomolny-Schmit heuristics. |
| title | Fluctuations in the number of nodal domains |
| topic | Probability Mathematical Physics Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2006.07730 |