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July, 2005 Correlation functions of the shifted Schur measure
J. Math. Soc. Japan 57(3): 619-637 (July, 2005). DOI: 10.2969/jmsj/1158241925


The shifted Schur measure introduced in [TW2] is a measure on the set of all strict partitions, which is defined by Schur Q -functions. The main aim of this paper is to calculate the correlation function of this measure, which is given by a pfaffian. As an application, we prove that a limit distribution of parts of partitions with respect to a shifted version of the Plancherel measure for symmetric groups is identical with the corresponding distribution of the original Plancherel measure. In particular, we obtain a limit distribution of the length of the longest ascent pair for a random permutation. Further we give expressions of the mean value and the variance of the size of partitions with respect to the measure defined by Hall-Littlewood functions.


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Sho MATSUMOTO. "Correlation functions of the shifted Schur measure." J. Math. Soc. Japan 57 (3) 619 - 637, July, 2005.


Published: July, 2005
First available in Project Euclid: 14 September 2006

zbMATH: 1078.60010
MathSciNet: MR2139724
Digital Object Identifier: 10.2969/jmsj/1158241925

Primary: 60C05
Secondary: 05E05

Keywords: ascent pair , correlation functions , Hall-Littlewood functions , limit distributions , Plancherel measures , Random permutations , Schur Q-functions , shifted Schur measure , Tracy-Widom distribution

Rights: Copyright © 2005 Mathematical Society of Japan


Vol.57 • No. 3 • July, 2005
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