Geometric and Functional Analysis

, Volume 25, Issue 4, pp 1258–1289 | Cite as

Towards large genus asymptotics of intersection numbers on moduli spaces of curves

  • Maryam Mirzakhani
  • Peter Zograf


We explicitly compute the diverging factor in the large genus asymptotics of the Weil–Petersson volumes of the moduli spaces of n-pointed complex algebraic curves. Modulo a universal multiplicative constant we prove the existence of a complete asymptotic expansion of the Weil–Petersson volumes in the inverse powers of the genus with coefficients that are polynomials in n. This is done by analyzing various recursions for the more general intersection numbers of tautological classes, whose large genus asymptotic behavior is also extensively studied.


Modulus Space Intersection Number Inverse Power Riemann Zeta Function Ratio Versus 
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© Springer Basel 2015

Authors and Affiliations

  1. 1.Department of MathematicsStanford UniversityStanfordUSA
  2. 2.St. Petersburg Department, Steklov Mathematical InstituteSt. PetersburgRussia
  3. 3.Chebyshev LaboratorySt. Petersburg State UniversitySt. PetersburgRussia

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