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HYDRODYNAMIC LIMIT FOR THE PLANCHEREL ENSEMBLE OF YOUNG DIAGRAMS AND FREE PROBABILITY

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/84200

Title: HYDRODYNAMIC LIMIT FOR THE PLANCHEREL ENSEMBLE OF YOUNG DIAGRAMS AND FREE PROBABILITY
Authors: HORA, Akihito Browse this author
Keywords: hydrodynamic limit
Young diagram
symmetric group
free probability
Markov chain
Plancherel measure
Kerov polynomial.
Issue Date: 26-May-2014
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 1056
Start Page: 1
End Page: 28
Abstract: Concentration phenomena in statistical ensembles of Young diagrams have been investigated as static models first for the Plancherel ensemble by Vershik–Kerov and Logan–Shepp in 1970s and later for some other group-theoretical ensembles by Biane. On the other hand, a dynamical model of concentration for Young diagrams, which is not directly connected with group representations, was shown by Funaki– Sasada in the framework of hydrodynamic limit. Our aim here is to discuss a dynamical model of concentration for Young diagrams in grouptheoretical ensembles. We especially feature Biane’s approximate factorization property of ensembles as an origin to give rise to concentration. Starting from an initial ensemble yielding concentration and a microscopic dynamics keeping the Plancherel measure invariant, we derive an evolution of rescaled shapes of Young diagrams through hydrodynamic limit. The resulting evolution along macroscopic time is described in terms of the notions of Voiculescu’s free probability theory such as free compression and free convolution of Kerov transition measures.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69860
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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