Correlation functions of the shifted Schur measure

The shifted Schur measure introduced in [TW2] is a measure on the set of all strict partitions λ = (λ1 > λ2 > · · · > λl > 0), 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 λj ’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 ([BDJ, BOO, J3, O1]). 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 |λ| with respect to the measure defined by Hall-Littlewood functions. 2000 Mathematics Subject Classification : Primary 60C05; Secondary 05E05.