Robinson--Schensted--Knuth Algorithm, Jeu de Taquin, and Kerov--Vershik Measures on Infinite Tableaux
Abstract
We investigate the Robinson--Schensted--Knuth algorithm (RSK) and Schützenberger's jeu de taquin in the infinite setup. We show that the recording tableau in RSK defines an isomorphism of the following two dynamical systems: (i) a sequence of independent and identically distributed random letters equipped with Bernoulli shift, and (ii) a random infinite Young tableau (with the distribution given by Vershik--Kerov measure, corresponding to some Thoma character of the infinite symmetric group) equipped with jeu de taquin transformation. As a special case we recover the results on noncolliding random walks and multidimensional Pitman transform.
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Submitted: 22 July 2013
Accepted: 23 January 2014
Published online: 8 April 2014
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