Virasoro constraints and Hurwitz numbers through asymptotic analysis

Abstract

We present a new method, using asymptotic analysis, to obtain a system of recursion relations for integrals on moduli spaces of curves. By applying the asymptotic analysis on the join-cut relation of the ELSV formula, we derive the recursion relation of R. Dijkgraaf and E. and H. Verlinde, which is exactly the Virasoro constraints for topological gravity. This gives an alternative proof of Witten�s Conjecture using asymptotic analysis.