On the VershikKerov Conjecture Concerning the ShannonMcMillanBreiman Theorem for the Plancherel Family of Measures on the Space of Young Diagrams
On the VershikKerov Conjecture Concerning the ShannonMcMillanBreiman Theorem for the Plancherel Family of Measures on the Space of Young Diagrams

Alexander Bufetov, Steklov Institute of Mathematics and Rice University
Fine Hall 801
Vershik and Kerov conjectured in 1985 that dimensions of irreducible representations of finite symmetric groups, after appropriate normalization, converge to a constant with respect to the Plancherel family of measures on the space of Young diagrams. The statement of the VershikKerov conjecture can be seen as an analogue of the ShannonMcMillanBreiman Theorem for the nonstationary Markov process of the growth of a Young diagram. The limiting constant is then interpreted as the entropy of the Plancherel measure. The main result of the paper is the proof of the VershikKerov conjecture. The argument is based on the methods of Borodin, Okounkov and Olshanski. The talk is based on the preprint arXiv:1001.4275