Correlation functions of the shifted Schur measure

MATSUMOTO, Sho

J. Math. Soc. Japan, Tome 57 (2005) no. 4, p. 619-637 / Harvested from Project Euclid

Résumé

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.

Détail

Publié le : 2005-07-14
Classification:  shifted Schur measure,  Schur Q-functions,  correlation functions,  limit distributions,  Plancherel measures,  ascent pair,  random permutations,  Hall-Littlewood functions,  Tracy-Widom distribution,  60C05,  05E05