On the large genus asymptotics of Weil-Petersson volumes

Abstract

A relatively fast algorithm for evaluating Weil-Petersson volumes of moduli spaces of complex algebraic curves is proposed. On the basis of numerical data, a conjectural large genus asymptotics of the Weil-Petersson volumes is computed. Asymptotic formulas for the intersection numbers involving $\psi$-classes are conjectured as well. The accuracy of the formulas is high enough to believe that they are exact.

Formula in Theorem 2 (iii) corrected, footnote added

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