Journal
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
Volume -, Issue -, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1742-5468/2008/07/P07023
Keywords
rigorous results in statistical mechanics; matrix models; topological expansion; topology and combinatorics
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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.
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