Correlation functions of the shifted Schur measure

Details Correlation functions of the shifted Schur measure Correlation functions of the shifted Schur measure

2003-12-19

arxiv.org/abs/math/0312373v2

J. Math. Soc. Japan, vol.57, no. 3 (2005), 619--637

Mathematics

Combinatorics

18 pages, the title of the first version is ``A limit distribution of the length of the longest ascent pair for a random permu

Scientific paper

The shifted Schur measure introduced by Tracy and Widom 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 $\lambda_j$'s with respect to a shifted version of the Plancherel measure for symmetric groups is identical with the corresponding distribution of the original Plancherel measure. Further we give expressions of the mean value and the variance of the size of a partition with respect to the measure defined by Hall-Littlewood functions.

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