2008/02/13 by Bertrand Eynard · 1 citation
Physics and Astronomy · Mathematics · #math-ph #hep-th #math.MP
paper · pdf · doi:10.1088/1126-6708/2009/03/003
published as JHEP 0903:003,2009 · 23 pages, Latex
arxiv created 2008/02/13 · arxiv updated 2009/12/01
We propose an asymptotic expansion formula for matrix integrals, including oscillatory terms (derivatives of theta-functions) to all orders. This formula is heuristically derived from the analogy between matrix integrals, and formal matrix models (combinatorics of discrete surfaces), after summing over filling fractions. The whole oscillatory series can also be resummed into a single theta function. We also remark that the coefficients of the theta derivatives, are the same as those which appear in holomorphic anomaly equations in string theory, i.e. they are related to degeneracies of Riemann surfaces. Moreover, the expansion presented here, happens to be independent of the choice of a background filling fraction.