Combinatorial Encoding of Bernoulli Schemes and the Asymptotic Behavior of Young Tableaux

摘要

We consider two examples of a fully decodable combinatorial encoding of Bernoulli schemes: the encoding via Weyl simplices and the much more complicated encoding via the RSK (Robinson-Schensted-Knuth) correspondence. In the first case, decodability is quite a simple fact, while in the second case, this is a nontrivial result obtained by D. Romik and P. Sniady and based on [2], [12], and other papers. We comment on the proofs from the viewpoint of the theory of measurable partitions; another proof, using representation theory and generalized Schur-Weyl duality, will be presented elsewhere. We also study a new dynamics of Bernoulli variables on P-tableaux and find the limit 3D-shape of these tableaux.