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Gaussian fluctuations for Plancherel partitions December 02, 2010 (02:00 PM PST - 03:00 PM PST)
Parent Program: --
Location: MSRI: Simons Auditorium
Speaker(s) Leonid Bogachev
Description Abstract: The limit shape of Young diagrams under the Plancherel measure
was found by Vershik & Kerov (1977) and Logan & Shepp (1977). We obtain a
central limit theorem for fluctuations of Young diagrams in the bulk of
the partition "spectrum". More specifically, under a suitable
(logarithmic) normalization, the corresponding random process converges
(in the FDD sense) to a Gaussian process with independent values. We also
discuss a link with an earlier result by Kerov (1993) on the convergence
to a generalized Gaussian process. The proof is based on poissonization of
the Plancherel measure and an application of a general central limit
theorem for determinantal point processes. Joint work with Zhonggen Su
(Zhejiang University, China).
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