The Expected Depth of Random Real Algebraic Plane Curves
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2021
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913049003163648 |
|---|---|
| author | Bayraktar, Turgay Kişisel, Ali Ulaş Özgür |
| author_facet | Bayraktar, Turgay Kişisel, Ali Ulaş Özgür |
| contents | In this note we study asymptotic isotopy of random real algebraic plane curves. More precisely, we obtain a Kac-Rice type formula that gives the expected number of two-sided components (i.e.\ ovals) of a random real algebraic plane curve winding around a given point. In particular, we show that expected number of such ovals for an even degree Kostlan polynomial is $\frac{\sqrt{d}}{2}$ and independent of the given point. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_03198 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The Expected Depth of Random Real Algebraic Plane Curves Bayraktar, Turgay Kişisel, Ali Ulaş Özgür Algebraic Geometry Complex Variables Probability In this note we study asymptotic isotopy of random real algebraic plane curves. More precisely, we obtain a Kac-Rice type formula that gives the expected number of two-sided components (i.e.\ ovals) of a random real algebraic plane curve winding around a given point. In particular, we show that expected number of such ovals for an even degree Kostlan polynomial is $\frac{\sqrt{d}}{2}$ and independent of the given point. |
| title | The Expected Depth of Random Real Algebraic Plane Curves |
| topic | Algebraic Geometry Complex Variables Probability |
| url | https://arxiv.org/abs/2110.03198 |