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 geometry of random polygons

## The geometry of random polygonsAdd to your list(s) Download to your calendar using vCal - Shonkwiler, C (University of Georgia)
- Thursday 06 December 2012, 09:20-09:40
- 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 What is the expected shape of a ring polymer in solution? This is a natural question in statistical physics which suggests an equally interesting mathematical question: what are the statistics of the geometric invariants of random, fixed-length n-gons in space? Of course, this requires first answering a more basic question: what is the natural metric (and corresponding probability measure) on the compact manifold of fixed-length n-gons in space modulo translation? In this talk I will describe a natural metric on this space which is pushed forward from the standard metric on the Stiefel manifold of 2-frames in complex n-space via the coordinatewise Hopf map introduced by Hausmann and Knutson. With respect to the corresponding probability measure it is then possible to prove very precise statements about the statistical geometry of random polygons. For example, I will show that the expected radius of gyration of an n-gon sampled according to this measure is exactly 1/(2n). I will also demonstrate a simple, linear-time algorithm for directly sampling polygons from this measure. This is joint work with Jason Cantarella (University of Georgia, USA ) and Tetsuo Deguchi (Ochanomizu University, Japan). 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 listsComputer Laboratory Programming Research Group Seminar Sir Richard Stone Annual Lecture Wall Street meets Lincoln's Inn!## Other talksAlexander Ogg (1811-65): surveyor, farmer and gold prospector, Aberdeenshire and New Zealand Why We Disagree about Human Nature Virginia Woolf's To the Lighthouse 'The River Ganges running red: reversing the divine' Mobile elements, polydactyl proteins and the species-specificity of human biology Predictive Multiscale Modeling for Decision Support in Design of Hierarchical Alloy Systems |