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SUMMARY:Persi Diaconis (Stanford University)
DTSTART:20201013T130000Z
DTEND:20201013T140000Z
DTSTAMP:20260423T004643Z
UID:PSA/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/PSA/1/">The 
 Mathematics of making a mess (an introduction to random walk on groups)</a
 >\nby Persi Diaconis (Stanford University) as part of Probability and Stoc
 hastic Analysis at Tecnico Lisboa\n\n\nAbstract\nHow many random transposi
 tions does it take to mix up $n$ cards? This is a typical question of rand
 om walk on finite groups. The answer is $\\frac{1}{2}n \\log{n} + Cn$ and 
 there is a sharp phase transition from order to chaos as $C$ varies. The t
 echniques involve Fourier analysis on non-commutative groups (which I will
  try to explain for non specialists). As you change the group or change th
 e walk\, new analytic and algebraic tools are required. The subject has wi
 de applications (people still shuffle cards\, but there are applications i
 n physics\, chemistry\,biology and computer science — even for random tr
 anspositions). Extending to compact or more general groups opens up many p
 roblems. This was the first problem where the ‘cutoff phenomenon’ was 
 observed and this has become a healthy research area.\n
LOCATION:https://researchseminars.org/talk/PSA/1/
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