Robinson--Schensted--Knuth Algorithm, Jeu de Taquin, and Kerov--Vershik Measures on Infinite Tableaux

We investigate the Robinson--Schensted--Knuth algorithm (RSK) and Schutzenberger'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 lette...

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Published inSIAM journal on discrete mathematics Vol. 28; no. 2; pp. 598 - 630
Main Author Sniady, Piotr
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.01.2014
Subjects
Algorithms
Applied mathematics
Correspondence
Dynamical systems
Group theory
Mathematical analysis
Probability
Random walk
Recording
Transformations
Transforms
Online AccessGet full text
ISSN0895-4801
1095-7146
DOI10.1137/130930169

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Abstract We investigate the Robinson--Schensted--Knuth algorithm (RSK) and Schutzenberger'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. [PUBLICATION ABSTRACT]
AbstractList We investigate the Robinson--Schensted--Knuth algorithm (RSK) and Schutzenberger'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. [PUBLICATION ABSTRACT]
We investigate the Robinson--Schensted--Knuth algorithm (RSK) and Schutzenberger'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.
Author Śniady, Piotr
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10.1016/0022-4049(85)90042-8
10.1007/BF01114877
10.1137/0607014
10.1023/A:1021177012548
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Snippet We investigate the Robinson--Schensted--Knuth algorithm (RSK) and Schutzenberger's jeu de taquin in the infinite setup. We show that the recording tableau in...
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SubjectTerms Algorithms
Applied mathematics
Correspondence
Dynamical systems
Group theory
Mathematical analysis
Probability
Random walk
Recording
Transformations
Transforms
Title Robinson--Schensted--Knuth Algorithm, Jeu de Taquin, and Kerov--Vershik Measures on Infinite Tableaux
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