All order asymptotic expansion of large partitions

The generating function which counts partitions with the Plancherel measure (and its q-deformed version) can be rewritten as a matrix integral, which allows one to compute its asymptotic expansion to all orders. There are applications in the statistical physics of growing/melting crystals, TASEP ( totally asymmetric exclusion processes), and also algebraic geometry. In particular we compute the Gromov-Witten invariants of the X-p = O(p - 2) circle plus O(-p) -> P-1 Calabi-Yau threefold, and we prove a conjecture of Marino, that the generating functions F-g of Gromov-Witten invariants of X-p come from a matrix model, and are the symplectic invariants of the mirror spectral curve.