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arXiv · 2110.03198

The Expected Depth of Random Real Algebraic Plane Curves

Turgay Bayraktar·Ali Ulaş Özgür Kişisel
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Abstract

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.

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BibTeXRIS

Turgay Bayraktar, Ali Ulaş Özgür Kişisel. 2021-10-07. The Expected Depth of Random Real Algebraic Plane Curves. https://arxiv.org/abs/2110.03198

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