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:  <http://ie.technion.ac.il/seminar_files/1301237501_B.pdf>

Or just see it here:
 
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.)
 
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