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arXiv · 1001.4275

On the Vershik-Kerov Conjecture Concerning the Shannon-McMillan-Breiman Theorem for the Plancherel Family of Measures on the Space of Young Diagrams

Alexander I. Bufetov
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Abstract

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 Vershik-Kerov conjecture can be seen as an analogue of the Shannon-McMillan-Breiman Theorem for the non-stationary 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 Vershik-Kerov conjecture. The argument is based on the methods of Borodin, Okounkov and Olshanski.

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Alexander I. Bufetov. 2012-06-15. On the Vershik-Kerov Conjecture Concerning the Shannon-McMillan-Breiman Theorem for the Plancherel Family of Measures on the Space of Young Diagrams. https://arxiv.org/abs/1001.4275

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