Mathematics – Probability
Scientific paper
2011-11-02
Mathematics
Probability
60 pages
Scientific paper
We study an infinite version of the jeu de taquin sliding game, which can be thought of as a natural measure-preserving transformation on the set of infinite Young tableaux equipped with the Plancherel probability measure. We use methods from representation theory to show that the Robinson-Schensted-Knuth (RSK) algorithm gives an isomorphism between this measure-preserving dynamical system and the one-sided shift dynamics on a sequence of independent and identically distributed random variables distributed uniformly on the unit interval. We also show that the jeu de taquin paths induced by the transformation are asymptotically straight lines emanating from the origin in a random direction whose distribution is computed explicitly, and show that this result can be interpreted as a statement on the limiting speed of a second-class particle in the Plancherel-TASEP particle system (a variant of the Totally Asymmetric Simple Exclusion Process associated with Plancherel growth), in analogy with earlier results for second class particles in the ordinary TASEP. Key words: jeu de taquin, Young tableau, Plancherel measure, TASEP, exclusion process, second class particle, dynamical system, isomorphism of measure preserving systems, representation theory of symmetric groups
Romik Dan
Sniady Piotr
No associations
LandOfFree
Jeu de taquin dynamics on infinite Young tableaux and second class particles does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Jeu de taquin dynamics on infinite Young tableaux and second class particles, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Jeu de taquin dynamics on infinite Young tableaux and second class particles will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-329684