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DTSTART:19700329T010000
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CATEGORIES:Probability
SUMMARY:Random tournaments - Brett Kolesnik (Oxford)
DTSTART;TZID=Europe/London:20230207T140000
DTEND;TZID=Europe/London:20230207T150000
UID:TALK197068AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/197068
DESCRIPTION:A tournament on a graph is an orientation of its e
dges. Vertices are players and each edge is a game
\, directed toward the winner. In this talk\, we w
ill discuss some recent results on random tourname
nts. With David Aldous (Berkeley) we construct ran
dom tournaments using Strassen’s coupling theorem\
, yielding a probabilistic proof of Moon's classic
al theorem. With Mario Sanchez (Cornell) we study
the geometry of random tournaments\, with its conn
ections to permutahedra\, zonotopes\, etc. We show
that the recent Coxeter permutahedra are related
to tournaments that involve collaboration (and com
petition\, as usual) answering a question of Stanl
ey. Finally\, we settle a conjecture of Takács abo
ut the asymptotic number of score sequences. The p
roof involves combinatorics (Erdős–Ginzburg–Ziv nu
mbers)\, renewal theory and infinitely divisible d
istributions.
LOCATION:MR12\, Centre for Mathematical Sciences
CONTACT:Perla Sousi
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