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We consider two examples of a fully decodable combinatorial encoding ofBernoulli schemes: the encoding via Weyl simplices and the much morecomplicated encoding via the RSK (Robinson--Schensted--Knuth) correspondence.In the first case, the decodability is a quite simple fact, while in the secondcase, this is a nontrivial result obtained by D.~Romik and P.~\'Sniady andbased on the papers~ \cite{KV}, \cite{VK}, and others. We comment on the proofsfrom the viewpoint of the theory of measurable partitions; another proof, usingrepresentation theory and generalized Schur--Weyl duality, will be presentedelsewhere. We also study a new dynamics of Bernoulli variables on $P$-tableauxand find the limit 3D-shape of these tableaux.

Combinatorial encoding of Bernoulli schemes and the asymptotic behavior of Young tableaux