|COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring.|
The Expected Total Curvature of Random Polygons
If you have a question about this talk, please contact Mustapha Amrani.
Topological Dynamics in the Physical and Biological Sciences
We consider the expected value for the total curvature of a random closed polygon. Numerical experiments have suggested that as the number of edges becomes large, the difference between the expected total curvature of a random closed polygon and a random open polygon with the same number of turning angles approaches a positive constant. We show that this is true for a natural class of probability measures on polygons, and give a formula for the constant in terms of the moments of the edgelength distribution.
We then consider the symmetric measure on closed polygons of fixed total length constructed by Cantarella, Deguchi, and Shonkwiler. For this measure, the expected total curvature of a closed n-gon is asymptotic to n pi/2 (2n/2n-3) pi/4. As a consequence, we show that at least 1/3 of fixed-length hexagons and 1/11 of fixed-length heptagons in 3-space are unknotted.
This talk is part of the Isaac Newton Institute Seminar Series series.
This talk is included in these lists:
Note that ex-directory lists are not shown.
Other listsCQIF Seminar Symposium on Computational Biology Whiston Society
Other talksTBC (molecular mechanisms of emphysema, hypoxia and lung aging) Self-efficacy in foreign language learning Mechanical forces in B cell activation Running Out of Energy? The Future of the UK’s Electricity Supply. Christina Koning, novelist The Development of Galaxies