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We show that Mirzakhani's recursions for the volumes of moduli space of Riemann surfaces are a special case of random matrix loop equations, and therefore we confirm again that Kontsevitch's integral is a generating function for those volumes.
M. Mirzakhani, “Simple geodesics and Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces”, Invent. Math. 167, 179-222 (2007)
2007
Earlier work this paper cites.
K. Liu, H. Xu, “A simple proof of Mirzakhani’s recursion formula of Weil-Petersson volumes”, math.AG/0705.2086
2086
Cited alongside, same era.
B. Eynard, “Topological expansion for the 1-hermitian matrix model correlation functions”, JHEP/024A/0904, hep-th/0407261
Cited in the paper.
B.Eynard, N.Orantin, “Invariants of algebraic curves and topological expansion”, math-ph/0702045
Cited in the paper.
M. Mulase, B. Safnuk, “Mirzakhani’s recursion relations, Virasoro constraints and the KdV hierarchy”, math.AG/0101147
Cited in the paper.
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