Technion, IEM faculty - Seminar in Probability and Stochastic Processes
Speaker: Leonid Bogachev (Leeds, UK)
Title: Gaussian fluctuations for Plancherel partitions
Date: 12/04/2011
Time: 11:30
Place: Hashmal-861
Abstract:  <>

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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.)
Technion Math. Net (TECHMATH)
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