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Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Statistics Seminars: Gaussian fluctuations for Plancherel partitions

Presented by Leonid Bogachev, Department of Statistics, University of Leeds

15 May 2009 16:15 in CM221

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, we prove that, under a suitable (logarithmic) normalisation, the corresponding random process converges (in the FDD sense) to a Gaussian process with independent values. We also discuss the link with an earlier result by Kerov (1993) on the convergence to a generalised Gaussian process. The proof is based on the poissonisation of the Plancherel measure and an application of a general central limit theorem for determinantal point processes. (Joint work with Zhonggen Su.)

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