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SUMMARY:Random tournaments - Brett Kolesnik (Oxford)
DTSTART:20230207T140000Z
DTEND:20230207T150000Z
UID:TALK197068@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:A tournament on a graph is an orientation of its edges. Vertic
 es are players and each edge is a game\, directed toward the winner. In th
 is talk\, we will discuss some recent results on random tournaments. With 
 David Aldous (Berkeley) we construct random tournaments using Strassen’s
  coupling theorem\, yielding a probabilistic proof of Moon's classical the
 orem. With Mario Sanchez (Cornell) we study the geometry of random tournam
 ents\, with its connections to permutahedra\, zonotopes\, etc. We show tha
 t the recent Coxeter permutahedra are related to tournaments that involve 
 collaboration (and competition\, as usual) answering a question of Stanley
 . Finally\, we settle a conjecture of Takács about the asymptotic number 
 of score sequences. The proof involves combinatorics (Erdős–Ginzburg–
 Ziv numbers)\, renewal theory and infinitely divisible distributions. 
LOCATION:MR12\, Centre for Mathematical Sciences
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