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SUMMARY:The combinatorics of spaghetti hoops - Professor Simon Tavaré  FR
 S FMedSci\, Department of Applied Mathematics and Theoretical  Physics and
  Cancer Research UK Cambridge Institute
DTSTART:20181119T180000Z
DTEND:20181119T190000Z
UID:TALK109843@talks.cam.ac.uk
CONTACT:Beverley Larner
DESCRIPTION:Starting with n cooked spaghetti strands\, tie randomly chosen
  ends together to produce a collection of spaghetti hoops. What is the exp
 ected number of hoops? What can be said about the distribution of the numb
 er of hoops of length 1\, 2\, …? What is the behaviour of the longest ho
 ops when n is large? What is the probability that all the hoops have diffe
 rent lengths? Questions like this appear in many guises in many areas of m
 athematics\, the connection being their relation to the Ewens Sampling For
 mula (ESF). I will describe a number of related examples\, including prime
  factorisation\, random mappings and random permutations\, illustrating th
 e central role played by the ESF. I will also discuss methods for simulati
 ng decomposable combinatorial structures by exploiting another wonder of t
 he ESF world\, namely the Feller Coupling. Analysis of a children’s play
 ground game shows that apparently small departures from the Feller model c
 an open up a number of unsolved problems. 
LOCATION:Bristol-Myers Squibb Lecture Theatre\, Department of Chemistry
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