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SUMMARY:The geometry of random polygons - Shonkwiler\, C (University of Ge
 orgia)
DTSTART:20121206T092000Z
DTEND:20121206T094000Z
UID:TALK41888@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:What is the expected shape of a ring polymer in solution? This
  is a natural question in statistical physics which suggests an equally in
 teresting mathematical question: what are the statistics of the geometric 
 invariants of random\, fixed-length n-gons in space? Of course\, this requ
 ires first answering a more basic question: what is the natural metric (an
 d corresponding probability measure) on the compact manifold of fixed-leng
 th n-gons in space modulo translation? \n\nIn this talk I will describe a 
 natural metric on this space which is pushed forward from the standard met
 ric on the Stiefel manifold of 2-frames in complex n-space via the coordin
 atewise Hopf map introduced by Hausmann and Knutson. With respect to the c
 orresponding probability measure it is then possible to prove very precise
  statements about the statistical geometry of random polygons. \n\nFor exa
 mple\, I will show that the expected radius of gyration of an n-gon sample
 d according to this measure is exactly 1/(2n). I will also demonstrate a s
 imple\, linear-time algorithm for directly sampling polygons from this mea
 sure. This is joint work with Jason Cantarella (University of Georgia\, US
 A) and Tetsuo Deguchi (Ochanomizu University\, Japan).\n
LOCATION:Seminar Room 1\, Newton Institute
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