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Transition distributions of young diagrams under periodically weighted plancherel measures

Transition distributions of young diagrams under periodically weighted plancherel measures Kerov[16,17] proved that Wigner’s semi-circular law in Gaussian unitary ensembles is the transition distribution of the omega curve discovered by Vershik and Kerov[34] for the limit shape of random partitions under the Plancherel measure. This establishes a close link between random Plancherel partitions and Gaussian unitary ensembles. In this paper we aim to consider a general problem, namely, to characterize the transition distribution of the limit shape of random Young diagrams under Poissonized Plancherel measures in a periodic potential, which naturally arises in Nekrasov’s partition functions and is further studied by Nekrasov and Okounkov[25] and Okounkov[28,29]. We also find an associated matrix model for this transition distribution. Our argument is based on a purely geometric analysis on the relation between matrix models and Seiberg-Witten differentials. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Transition distributions of young diagrams under periodically weighted plancherel measures

Acta Mathematicae Applicatae Sinica , Volume 25 (4) – Sep 8, 2009

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Publisher
Springer Journals
Copyright
Copyright © 2009 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer Berlin Heidelberg
Subject
Mathematics; Theoretical, Mathematical and Computational Physics; Math Applications in Computer Science; Applications of Mathematics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-008-8822-2
Publisher site
See Article on Publisher Site

Abstract

Kerov[16,17] proved that Wigner’s semi-circular law in Gaussian unitary ensembles is the transition distribution of the omega curve discovered by Vershik and Kerov[34] for the limit shape of random partitions under the Plancherel measure. This establishes a close link between random Plancherel partitions and Gaussian unitary ensembles. In this paper we aim to consider a general problem, namely, to characterize the transition distribution of the limit shape of random Young diagrams under Poissonized Plancherel measures in a periodic potential, which naturally arises in Nekrasov’s partition functions and is further studied by Nekrasov and Okounkov[25] and Okounkov[28,29]. We also find an associated matrix model for this transition distribution. Our argument is based on a purely geometric analysis on the relation between matrix models and Seiberg-Witten differentials.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Sep 8, 2009

References