All orders asymptotic expansion of large partitions
Mathematical Physics
2008-12-18 v2 Statistical Mechanics
High Energy Physics - Theory
math.MP
Abstract
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.
Cite
@article{arxiv.0804.0381,
title = {All orders asymptotic expansion of large partitions},
author = {Bertrand Eynard},
journal= {arXiv preprint arXiv:0804.0381},
year = {2008}
}
Comments
37 pages, latex, 10 figures, reference and example added, few misprints corrected