A Limit Theorem for Shifted Schur Measures

Abstract

To each partition $λ$ with distinct parts we assign the probability $Q_λ(x) P_λ(y)/Z$ where $Q_λ$ and $P_λ$ are the Schur $Q$-functions and $Z$ is a normalization constant. This measure, which we call the shifted Schur measure, is analogous to the much-studied Schur measure. For the specialization of the first $m$ coordinates of $x$ and the first $n$ coordinates of $y$ equal to $α$ ($0<α<1$) and the rest equal to zero, we derive a limit law for $λ_1$ as $m,n\ra\infty$ with $τ=m/n$ fixed. For the Schur measure the $α$-specialization limit law was derived by Johansson. Our main result implies that the two limit laws are identical.