COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |

University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > The Expected Total Curvature of Random Polygons

## The Expected Total Curvature of Random PolygonsAdd to your list(s) Download to your calendar using vCal - Cantarella, J (University of Georgia)
- Thursday 06 December 2012, 09:40-10:00
- Seminar Room 1, Newton Institute.
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 pi/4 by our first result. With a more careful analysis, we are able to prove that the exact expected value of total curvature is 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:- All CMS events
- Featured lists
- INI info aggregator
- Isaac Newton Institute Seminar Series
- School of Physical Sciences
- Seminar Room 1, Newton Institute
Note that ex-directory lists are not shown. |
## Other listsDarwin Humanities and Social Sciences Seminar Cambridge Rare Disease Network Buddhism Talk on Silent Illumination Meditation## Other talksOxidant-Activated PKGIα and Adaptation to Pulmonary Hypertension Are Sensor Networks a first step towards the Diamond Age? MRI: How can we help each other? New insights into clinical implications of cardiovascular ageing Dr Lindsay Hall: Early life microbiota-host interactions A short history of the microscope |