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SUMMARY:Zhonggen Su (Zhejiang University)
DTSTART:20201228T074500Z
DTEND:20201228T083000Z
DTSTAMP:20260423T023930Z
UID:iccm2020/63
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/iccm2020/63/
 ">Fluctuations on Plancherel interger partitions around its limit shape</a
 >\nby Zhonggen Su (Zhejiang University) as part of ICCM 2020\n\n\nAbstract
 \nFor s natural number n\, let P_n be the space of all integer partitions 
 \\lambda of n. Let P_{pl}(\\lambda)=\\frac{d_{\\lambda}^2}{n!}\, where d_{
 \\lambda} stands for the numbers of all standard Young tableanux with shap
 e \\lambda. A remarkable result\, almost simultaneously obtained by Logan 
 and Shepp\, Vershik and Kerov in the seventies\, is that there is a limit 
 shape w(x) for suitably scale \\lambda under the probability measure P_{pl
 }. In this talk we will report a Gaussian fluctuation result for \\lambda_
 {[\\sqrt{n}x]} around the shape curve w(x). The result complements\, in a 
 striking way\, the well-known theorem of Kerov on the generalized Gaussian
  convergence. The proofs are based on the poissonization techniques and th
 e Costin-Lebowitz-Soshnikov central limit theorem for determinantal point 
 processes.\n
LOCATION:https://researchseminars.org/talk/iccm2020/63/
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