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SUMMARY:Persi Diaconis (Stanford University)
DTSTART:20201013T130000Z
DTEND:20201013T140000Z
DTSTAMP:20260404T143400Z
UID:PSA/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/PSA/1
 /">The Mathematics of making a mess (an introduction to random walk on gro
 ups)</a>\nby Persi Diaconis (Stanford University) as part of Probability a
 nd Stochastic Analysis at Tecnico Lisboa\n\n\nAbstract\nHow many random tr
 anspositions does it take to mix up $n$ cards? This is a typical question 
 of random walk on finite groups. The answer is $\\frac{1}{2}n \\log{n} + C
 n$ and there is a sharp phase transition from order to chaos as $C$ varies
 . The techniques involve Fourier analysis on non-commutative groups (which
  I will try to explain for non specialists). As you change the group or ch
 ange the walk\, new analytic and algebraic tools are required. The subject
  has wide applications (people still shuffle cards\, but there are applica
 tions in physics\, chemistry\,biology and computer science — even for ra
 ndom transpositions). Extending to compact or more general groups opens up
  many problems. This was the first problem where the ‘cutoff phenomenon
 ’ was observed and this has become a healthy research area.\n
LOCATION:https://stable.researchseminars.org/talk/PSA/1/
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