All orders asymptotic expansion of large partitions

Details All orders asymptotic expansion of large partitions All orders asymptotic expansion of large partitions

2008-04-02

arxiv.org/abs/0804.0381v2

J.Stat.Mech.0807:P07023,2008

Physics

Mathematical Physics

37 pages, latex, 10 figures, reference and example added, few misprints corrected

Scientific paper

10.1088/1742-5468/2008/07/P07023

The generating function which counts partitions with the Plancherel measure (and its q-deformed version), can be rewritten as a matrix integral, which allows to compute its asymptotic expansion to all orders. There are applications in statistical physics of growing/melting crystals, T.A.S.E.P., and also in algebraic geometry. In particular we compute the Gromov-Witten invariants of the X_p Calabi-Yau 3-fold, and we prove a conjecture of M. 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.

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