Generating functions for intersection numbers on moduli spaces of curves

Abstract

Using the connection between intersection theory on the Deligne-Mumford spaces and the edge scaling of the GUE matrix model (see math.CO/9903176, math.AG/0101147), we express the n-point functions for the intersection numbers as n-dimensional error-function-type integrals and also give a derivation of Witten's KdV equations using the higher Fay identities of Adler, Shiota, and van Moerbeke.

Latex, 27 pages, 2 figures

References in corpus (4)

• Level-Spacing Distributions and the Airy Kernel
• 2D Gravity and Random Matrices
• Gromov-Witten theory, Hurwitz numbers, and Matrix models, I
• Logarithmic series and Hodge integrals in the tautological ring (with an appendix by D. Zagier)

Cited by in corpus (10)

• Free Energy from Replica Wormholes
• Explorations of Non-Perturbative JT Gravity and Supergravity
• Correlation functions of the KdV hierarchy and applications to intersection numbers over ${\overline{\mathcal{M}}}_{g,n}$
• From Brezin-Hikami to Harer-Zagier formulas for Gaussian correlators
• On Free Energy for Deformed JT Gravity
• The rank of a hypergeometric system
• Kontsevich-Witten Model From 2+1 Gravity: New Exact Combinatorial Solution
• On an Airy matrix model with a logarithmic potential
• The intersection numbers of the p-spin curves from random matrix theory
• Faces of matrix models