  We establish an isomorphism between the center of the Heisenberg category
defined by Khovanov and the algebra $\Lambda^*$ of shifted symmetric functions
defined by Okounkov-Olshanski. We give a graphical description of the shifted
power and Schur bases of $\Lambda^*$ as elements of the center, and describe
the curl generators of the center in the language of shifted symmetric
functions. This latter description makes use of the transition and
co-transition measures of Kerov and the noncommutative probability spaces of
Biane.
